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•I

ELECTRIC WAVES

•ELECTEIC WAVES'

BEING

RESEARCHES ON THE PROPAGATION OF ELECTRIC

ACTION WITH FINITE VELOCITY

THROUGH SPACE

BY U:-Mx^

Dr. HEINRICH HERTZ

FROFISSOB OF PHTSICS IH THE UHITBRSITT OF BOHH

AUTHORISED ENGLISH TRANSLATION

By D. K JONES, B.Sc.

DIRECTOR OF TECHNICAL EDUCATION TO THE STAPFORDSHIRE OOUlTrT COUNCIL
LATELY PROFESSOR OF PHTSICS IN THE UNIVERSITY COLLBOE OF WALES, ABERYSTWYTH

WITH A PREFACE BY LORD KELVIN, LL.D., D.C.L.

PRESIDENT OF THE ROYAL SOCIETY, PROFESSOR OF NATURAL PHILOSOPHY
IN THE UNIVERSITY OF GLASOOW, AND FELLOW OF ST. PBTER'S

COLLEGE, CAMBRIDGE

NIVERSIT

2.ontron
MACMILLAN AND CO.

AND NEW YORK
1893

^(p^S^f

BY THE AUTHOR

HIS EXCELLENCY

HERMANN VON HELMHOLTZ

WITH THE DEEPEST RESPECT AND ORATITUDE

UNIVERSITT)

TRANSLATOR'S NOTE

The publishers of Wiedemann's AnncUen^ being unable to
comply with the numerous applications made for copies of
Professor Hertz's researches, invited him to prepare his papers
for publication in a collected form. To recast or thoroughly
revise them would have been a serious undertaking; and
researches are most easily understood when described from the
standpoint from which they are undertaken. It was therefore
felt best to reprint the separate papers in the form in which
they were originally published; but Professor Hertz for-
tunately decided to supplement the papers by explanatory
notes, and to write an Introduction, in which he describes the
manner in which the investigations were undertaJ^en, and also
discusses their bearing upon electrical theory and the criticisms
to which they have been subjected. The collected researches
were published early last year under the title, UrUersuchungen
uber die Avsbreitung der Mektrischen Kraft.

The book now presented to the English reader is a transla-
tion of the German original, with only one or two slight alter-
ations in the notes, and a change, suggested by Lord Kelvin, in
the title. I would scarcely have undertaken the translation
if I had not been able to rely upon the supervision and kind
assistance which Professor Hertz has most freely given, and
for which my heartiest thanks are due. I have had the

viii translator's note

advantage of revising the proofs with him in Bonn, and now
trust that no serious error will have escaped notice.

For advice and help in seeing the book through the press,
I am indebted to several friends ; but most especially to Dr.
Philipp Lenard, Privat-docent in the University of Bonn. Dr.
Lenard has not only read and revised the translation from
start to finish, but has shown as keen an interest in it as if it
were his own work. I am very glad to have this opportunity
of acknowledging his valuable assistance, and of thanking him
most warmly for his kindness.

D. E. JONES.

Staffokd, December 1893.

PREFACE TO THE ENGLISH EDITION

To fully appreciate the work now ofifered to the English
reading public, we must carry our minds back two hundred
years to the time when Newton made known to the world the
law of universal gravitation. The idea that the sun pulls
Jupiter, and Jupiter pulls back against the sun with equal
force, and that the sun, earth, moon, and planets all act on
one another with mutual attractions seemed to violate the
supposed philosophic principle that matter cannot act where it
is not. The explanation of the motions of the planets by a
mechanism of crystal cycles and epicycles seemed natural and
intelligible, and the improvement on this mechanism invented
by Descartes in his vortices was no doubt quite satisfactory to
some of the greatest of Newton's scientific contemporaries.
Descartes's doctrine died hard among the mathematicians and
philosophers of continental Europe ; and for the first quarter
of last century belief in universal gravitation was an insularity
of our countrymen.

Voltaire, referring to a visit which he made to England in
1727, wrote: "A Frenchman who arrives in London finds a
great alteration in philosophy, as in other things. He left the
world full ; he finds it empty. At Paris you see the universe
composed of vortices of subtile matter; at London we see
nothing of the kind. With you it is the pressure of the
moon which causes the tides of the sea ; in England it is the
sea which gravitates towards the moon. . . . You will observe
also that the sun, which in France has nothing to do with the
business, here comes in for a quarter of it. Among you Car-
tesians all is done by impulsion ; with the Newtonians it is
done by an attraction of which we know the cause no better." ^

^ WheweU's History of the Lvductive Sciences, vol. ii. pp. 202, 203.

X PREFACE TO THE ENGLISH EDITION

Indeed, the Newtonian opinions had scarcely any disciples in
France till Voltaire asserted their claims on his return from
England in 1728. TUl then, as he himself says, there were
not twenty Newtonians out of England.^

In the second quarter of the century sentiment and'
opinion in France, Germany, Switzerland, and Italy ex-
perienced a great change. * The mathematical prize questions
proposed by the French Academy naturally brought the two
sets of opinions into conflict.' A Cartesian memoir of John
Bernoulli was the one which gained the prize in 1730. It
not infrequently happened that the Academy, as if desirous to
show its impartiality, divided the prize between Cartesians and
Newtonians. Thus, in 1734, the question being the cause of
the inclination of the orbits of the planets, the prize was shared
between John Bernoulli, whose memoir was founded on the
system of vortices, and his son Daniel, who was a Newtonian.^
The last act of homage of this kind to the Cartesian system
was performed in 1740, when the prize on the question of the
tides was distributed between Daniel Bernoulli, Euler, Mac-
laurin, and Cavallieri ; the last of whom had tried to amend
and patch up the Cartesian hypothesis on this subject.^

On the 4th February 1744 Daniel Bernoulli wrote as
follows to Euler : 'Uebrigens glaube ich, dass der Aether sowohl
gravis versus solem, als die Luft versus terram sey, und kann
Ihnen nicht bergen, dass ich uber diese Puncte ein volliger
Newtonianer bin, und verwundere ich mich, dass sie den Prin-
cipiis Cartesianis so lang adhariren ; es mochte wohl einige
Passion vielleicht mit unterlaufen. Hat Gott konnen eine
animam, deren Natur uns unbegreiflich ist, erschaflfen, so hat er
auch konnen eine attractionem universalem materiae imprimiren,
wenn gleich solche attractio supra captum ist, da hingegen die
Principia Cartesiana allzeit contra captum etwas involviren."

Here the writer, expressing wonder that Euler had so long
adhered to the Cartesian principles, declares himself a thorough-
going Newtonian, not merely in respect to gravitation versus
vortices, but in believing that matter may have been created
simply with the law of universal attraction without the aid of
any gravific medium or mechanism. But in this he was more
Newtonian than Newton himself.

^ Whe well's History of the Indv/ctive Sciences, vol. ii. p. 201. ^ Ihid, pp. 198,199.

PREFACE TO THE ENGLISH EDITION xi

Indeed Newton was not a Newtonian, according to Daniel
Bernoulli's idea of Newtonianism, for in his letter to Bentley of
date 25tli February 1692/ he wrote : " That gravity should be
innate, inherent, and essential to matter, so that one body may
act upon another at a distance through a > vacuum without the
mediation of anything else, by and through which their action
and force may be conveyed from one to another, is to me so
great an absurdity that I believe no man who has in philo-
sophical matters a competent faculty of thinking, can ever fall
into it." Thus Newton, in giving out his great law, did not
abandon the idea that matter cannot act where it is not. In
respect, however, merely of philosophic thought, we must feel
that Daniel Bernoulli was right ; we can conceive the sun
attracting Jupiter, and Jupiter attracting the sun, without any
intermediate medium, if they are ordered to do so. But the
question remains — ^Are they so ordered ? Nevertheless, 1 be-
' lieve all, or nearly all, his scientific contemporaries agreed with
Daniel Bernoulli in answering this question affirmatively.
Very soon after the middle of the eighteenth century Father
Boscovich ^ gave his brilliant doctrine (if infinitely improbable
theory) that elastic rigidity of solids, the elasticity of com-
pressible liquids and gases, the attractions of chemical affinity
and cohesion, the forces of electricity and magnetism ; in short,
all the properties of matter except heat, which he attributed
to a sulphureous essence, are to be explained by mutual
attractions and repulsions, varying solely with distances,
between mathematical points endowed also, each of them, with
inertia. Before the end of the eighteenth century the idea of
action-at-a-distance through absolute vacuum had become so
firmly established, and Boscovich's theory so unqualifiedly
accepted as a reality, that the idea of gravitational force or
electric force or magnetic force being propagated through and
by a medium, seemed as wild to the naturalists and mathe-
maticians of one hundred years ago as action-at-a-distance
had seemed to Newton and his contemporaries one hundred
years earlier. But a retrogression from the eighteenth century
school of science set in early in the nineteenth century.

^ The CorrespoTuUnce of Ricluird Bentley, D.D., vol. i. p. 70.

^ TJieoria Philoaophice Naturalis redacta ad unicam legem virium in natv/ra
existerUium atictore P, Jtogerio Josepho Boscovich^ Sodetatis Jeau, first edition,
Vienna, 1758. Second edition, amended and rTtrndpl hTtl1rl^^lltlMU Yi iiii ( , 1763.

Xli PREFACE TO THE ENGLISH EDITION

Faraday, with his curved lines of electric force, and his
dielectric efficiency of air and of liquid and solid insulators,
resuscitated the idea of a medium through which, and not only
through which but hy which, forces of attraction or repulsion,
seemingly acting at a distance, are transmitted. The long
struggle of the first half of the eighteenth century was not
merely on the question of a medium to serve for gravific
mechanism, but on the correctness of the Newtonian law of
gravitation as a matter of fact however explained. The
corresponding controversy in the nineteenth century was very
short, and it soon became obvious that Faraday's idea of the
transmission of electric force by a medium not only did not
violate Coulomb's law of relation between force and distance,
but that, if real, it must give a thorough explanation of that
law.^ Nevertheless, after Faraday's discovery^ of the different
specific inductive capacities of different insulators, twenty years
passed before it was generally accepted in continental Europe.
But before his death, in 1867, he had succeeded in inspiring
the rising generation of the scientific world with something
approaching to faith that electric force is transmitted by a
medium called ether, of which, as had been believed by the
whole scientific world for forty years, light and radiant heat
are transverse vibrations. Faraday himself did not rest with
this theory for electricity alone. The very last time I saw him
at work in the Eoyal Institution was in an underground cellar,
which he had chosen for freedom from disturbance ; and he
was arranging experiments to test the time of propagation of
magnetic force from an electromagnet through a distance of
many yards of air to a fine steel needle polished to reflect light ;
but no result came from those experiments. About the same
time or soon after, certainly not long before the end of his
working time, he was engaged (I believe at the shot tower near
Waterloo Bridge on the Surrey side) in efforts to discover
relations between gravity and magnetism, which also led to no
result.

Absolutely nothing has hitherto been done for gravity
either by experiment or observation towards deciding between

^ Electrostatics and Magnetism, Sir W. Thomson, Arts. I. (1842) and II.
(1845), particularly § 25 of Art. II.

2 1837. JEx^rimental Researches, 1161-1306.

PREFACE TO THE ENGUSH EDITION XIU

Newton and Bernoulli, as to the question of its propagation
through a medium, and up to the present time we have
no light, even so much as to point a way for investigation in
that direction. But for electricity and magnetism Faraday's
anticipations and Clerk-Maxwell's splendidly developed theory
have been established on the sure basis of experiment by Hertz's
work, of which his own most interesting account is now pre-
sented to the English reader by his translator, Professor D.
E. Jones. It is interesting to know, as Hertz explains in his
introduction, and it is very important in respect to the experi-
mental demonstration of magnetic waves to which he was led,
that he began his electric researches in a problem happily put
before him thirteen years ago by Professor von Helmholtz,
of which the object was to find by experiment some relation
between electromagnetic forces^ and dielectric polarisation of
insulators, without, in the first place, any idea of discovering a
progressive propagation of those forces through space.

It was by sheer perseverance in philosophical experimenting
that Hertz was led to discover (VII., p. 107 below) a finite
velocity of propagation of electromagnetic action, and then to
pass on to electromagnetic waves in air and their reflection
(VIII.), and to be able to say, as he says in a short reviewing
sentence at the end of VIII. : " Certainly it is a fascinating
idea that the processes in air which we have been investigating,
represent to us on a million-fold larger scale the same pro-
cesses which go on in the neighbourhood of a Fresnel
mirror or between the glass plates used for exhibiting
Newton's rings."

Pi'ofessor Oliver Lodge has done well, in connection with
Hertz's work, to call attention ^ to old experiments, and ideas
taken from them, by Joseph Henry, which came more nearly
to an experimental demonstration of electromagnetic waves
than anything that had been done previously. Indeed Henry,
after describing experiments showing powerful enough induction
due to a single spark from the prime conductor of an electric
machine to magnetise steel needles at a distance of 30 feet in
a cellar beneath with two floors and ceilings intervening, says
that he is " disposed to adopt the hypothesis of an electrical
plenum," and concludes with a short reviewing sentence, " It

* Modem Views of Electricity y pp. 369-372.

XIV PREFACE TO THE ENGLISH EDITION

may be further inferred that the diffusion of motion in this
case is almost comparable with that of a spark from a flint and
steel in the case of light."

Professor Oliver Lodge himself did admirable work in his
investigations regarding lightning rods,^ coming very near to
experimental demonstration of electromagnetic waves ; and he
drew important lessons regarding " electrical surgings " in an
insulated bar of metal " induced by Maxwell's and Heaviside's
electromagnetic waves," and many other corresponding pheno-
mena manifested both in ingenious and excellent experiments
devised by himself and in natural effects of lightning.

Of electrical surgings or waves in a short insulated wire,
and of interference between ordinary and reflected waves, and
positive electricity appearing where negative might have been
expected, we hear first it seems in Herr von Bezold's
"Eesearches on the Electric Discharge" (1870), which Hertz
gives as the Third Paper in the present series, with interesting
and ample recognition of its importance in relation to his own
great work.

Eeaders of the present volume will, I am sure, be pleased
if I call their attention to two papers by Prof. G. F. Fitzgerald
which I heard myself at the meeting of the British Association
at Southport in 1883. One of them is entitled, "On a
Method of producing Electromagnetic Disturbances of com-
paratively Short Wave-lengths." The paper itself is not long,
and I quote it here in full, as it appeared in the Uefport
of the British Association^ 1883: "This is by utilising the
alternating currents produced when an accumulator is dis-
charged through a small resistance. It is possible to produce
waves of as little as two metres wave-length, or even less."
This was a brilliant and useful suggestion. Hertz, not knowing
of it, used the method ; and, making as little as possible of the
" accumulator," got waves of as little as twenty-four centimetres
wave-length in many of his fundamental experiments. The
title alone of the other paper, " On the Energy lost by Eadia-
tion from Alternating Currents," is in itself a valuable lesson
in the electromagnetic theory of light, or the undulatory theory
of magnetic disturbance. The reader of the present volume

^ Lightning Condiictors and Lightning Guards^ Oliver J. Lodge, D.Sc.,F.R.S.
Whittaker and Co.

PREFACE TO THE ENGLISH EDITION XV

will be interested in comparing it with the title of Hertz's
Eleventh Paper; but I cannot refer to this paper without
expressing the admiration and delight with which I see the
words "rectilinear propagation," "polarisation," "reflection,"
" refraction," appearing in it as sub-titles.

During the fifty-six years which have passed since Faraday
first ofifended physical mathematicians with his curved lines of
force, many workers and many thinkers have helped to build
up the nineteenth -century school of plenum, one ether for
light, heat, electricity, magnetism; and the German and
English volumes containing Hertz's electrical papers, given to
the world in the last decade of the century, will be a per-
manent monument of the splendid consummation now realised.

KELVIN.

CONTENTS

XIII. On the Fundamental Equations of Electromagnetics for
Bodies at Best

XIV. On the Fundamental Equation
Bodies in Motion

Supplementary Notes

Index to Names .

s OF Electromagnetics for

PAoa

I. Introduction —

A. Experimental ...... 1

B. Theoretical ...... 20

II. On Very Rapid Electric Oscillations . .29

III. From Herr W. Von Bezold's Paper : *' Researches on the

Electric Discharge— Preliminary Communication" . 54

IV. On an Effect of Ultra- Violet Light upon the Electric

Discharge ....... 63

V. On the Action of a Rectilinear Electric Oscillation

UPON A Neighbouring Circuit . . . .80

VI. On Electromagnetic Effects produced by Electrical

Disturbances in Insulators . . . .95

VII. On the Finite Velocity of Propagation of Electro-
magnetic Actions . . . . .107

VIII. On Electromagnetic Waves in Air and their Reflection . 124

IX- The Forces of Electric Oscillations, treated according

TO Maxwell's Theory ..... 137

X. On the Propagation of Electric "VTaves by Means of

Wires ........ 160

XI. On Electric Radiation . . . . . .172

XII. On the Mechanical Action of Electric Waves in Wires . 186

195

241
269
279

UNIVERSITY

INTRODUCTION
A. Experimental

I HAVE often been asked how I was first led to carry out the
experiments which are described in the following pages. The
general inducement was this. In the year 1879 the Berlin
Academy of Science had offered a prize for a research on the
following problem : — To establish experimentally any relation
between electromagnetic forces and the dielectric polarisation
of insulators — ^that is to say, either an electromagnetic force
exerted by polarisations in non-conductors, or the polarisation
of a non-conductor as an effect of electromagnetic induc-
tion. As I was at that time engaged upon electromagnetic
researches at the Physical Institute in Berlin, Herr von
Helmholtz drew my attention to this problem, and promised
that I should have the assistance of the Institute in case I
decided to take up the work. I reflected on the problem, and
considered what results might be expected under favourable
conditions by using the oscillations of Leyden jars or of open
induction-coils. The conclusion at which I arrived was
certainly not what I had wished for ; it appeared that any
decided effect could scarcely be hoped for, but only an action
lying just within the limits of observation^ I therefore gave
up the idea of working at the problem ; nor am I aware that
it has been attacked by anybody else. But in spite of having
abandoned the solution at that time, I still felt ambitious to
discover it by some other method ; and my interest in every-
thing connected with electric oscillations had become keener.
It was scarcely possible that I should overlook any new form

2 INTRODUCTION i

of such oscillations, in case a happy chance should bring such
within my notice.

Such a chance occurred to me in the spring of 1886, and
brought with it the special inducement to take up the follow-
ing researches. In the collection of physical instruments at
the Technical High School at Karlsruhe (where these researches
were carried out), I had found and used for lecture purposes a
pair of so-called Eiess or Knochenhauer spirals. I had been
surprised to find that it was not necessary to discharge large
batteries through one of these spirals in order to obtain
sparks in the other ; that small Leyden jars amply sufiBced for
this purpose, and that even the discharge of a small induction-
coil would do, provided it had to spring across a spark-gap.
In altering the conditions I came upon the phenomenon of
side-sparks which formed the starting-point of the following
research. At first I thought the electrical disturbances
would be too turbulent and irregular to be of any further
use ; but when I had discovered the existence of a neutral
point in the middle of a side -conductor, and therefore of
a clear and orderly phenomenon, I felt convinced that the
problem of the Berlin Academy was now capable of solution.
My ambition at the time did not go further than this. My
conviction was naturally strengthened by finding that the
oscillations with which I had to deal were regular. The first
of the papers here republished (" On very Eapid Electric
Oscillations ") gives, generally in the actual order of time, the
course of the investigation as far as it was carried out up to
the end of the year 1^86 and the beginning of 1887.

While this paper was in the press I learned that its contents
were not as new as I had believed them to be. The Geographical
Congress of April 1887 brought Herr W. von Bezold to Karls-
ruhe and into my laboratory. I spoke to him about my experi-
ments; he replied that years ago he had observed similar
phenomena, and he drew my attention to his " Researches on
the Electric Discharge," in vol. cxl. of Poggendorfif's Anncden.
This paper had entirely escaped me, inasmuch as its external
appearance seemed to indicate that it related to matters quite
other than electric oscillations, namely, Lichtenberg figures ;
indeed, it does not appear to have attracted such attention as
the importance of its contents merited. In an appendix to

I INTRODUCTION 3

my paper I acknowledged Herr von Bezold's prior claim to a
whole series of observations. In place of this appendix, I here,
with Herr von Bezold's kind consent, include as the second of
these papers that part of his communication which is of the
most immediate interest in the present connection. It may
now well be asked with surprise how it was possible that
results so important and so definitely stated should have
exercised no greater influence upon the progress of science ?
Perhaps the fact that Herr von Bezold described his com-
munication as a preliminary one may have something to do
with this.

I may here be permitted to record the good work done by
two English colleagues who at the same time as myself were
striving towards the same end. In the same year in which I
carried out the above research. Professor Oliver Lodge, in
Liverpool, investigated the theory of the lightning-conductor,
and in connection with this carried out a series of experiments
on the discharge of small condensers which led him on to the
observation of oscillations and waves in wires.v Inasmuch as
he entirely accepted Maxwell's views, and eagerly strove to
verify them, there can scarcely be any doubt that if I had
not anticipated him he would also have succeeded in
observing waves in air, and thus also in proving the pro-
pagation with time of electric force. Professor Fitzgerald,
in Dublin, had some years before endeavoured to predict,
with the aid of theory, the possibility of such waves, and
to discover the conditions for producing them. My own
experiments were not influenced by the researches of these
physicists, for I only knew of them subsequently. Nor,
indeed, do I believe that it would have been possible to
arrive at a knowledge of these phenomena by the aid of
theory alone. For their appearance upon the scene of our
experiments depends not only upon their theoretical possi-
bility, but also upon a^ _special^and_,aarpris ing jproperty
^f the electric snad^ which could not be foreseen by any
\theory.>

By means of the experiments already mentioned I had
succeeded in obtaining a method of exciting more rapid
electric disturbances than were hitherto at the disposal of
physicists. But before I could proceed to apply this method

4 INTRODUCTION i

to the examination of the behaviour of insulators, I had to
finish with another investigation. Soon after starting the
experiments I had been struck by a noteworthy reciprocal action
between simultaneous electrical sparks. I had no intention
of allowing this phenomenon to distract my attention from
the main object which I had in view ; but it occurred in such
a definite and perplexing way that I could not altogether
neglect it. For some time, indeed, I was in doubt whether
I had not before me an altogether new form of electrical
action-at-a-distance. The supposition that the action was due
to light seemed to be excluded by the fact that glass plates cut
it off; and naturally it was some time before I came to experi-
ment with plates of rock-crystal. As soon as I knew for
certain that I was only dealing with an effect of ultra-violet
light, I put aside this investigation so as to direct my
attention once more to the main question. Inasmuch as a
certain acquaintance with the phenomenon is required in
investigating the oscillations, I have reprinted the communi-
cation relating to it (" On an Effect of Ultra -Violet Light
upon the Electric Discharge ") as the fourth of these papers.
A number of investigators, more especially Herren Eighi,
Hallwachs, and Elster and Geitel, have helped to make our
knowledge of the phenomenon more accurate; nevertheless,
the mechanics of it have not yet * been completely disclosed
to our understanding.

The summer of 1887 was spent in fruitless endeavours
to establish the electromagnetic influence of insulators by the
aid of the new class of oscillations. \ The simplest method con-
sisted in determining the effect of dielectrics upon the position
of the neutral point of a side-circuit. But in that case
I should have had to include the electrostatic forces in the
bargain, whereas the problem consisted precisely in investi-
gating the electromagnetic induction alone. The plan which
I adopted was the following : — The primary conductor ^ had
the form shown in Fig. 1 ; between the plates A and A^ at
its ends was introduced a block £B of sulphur or paraffin,
and this was then quickly removed. I placed the secondary
conductor in the same position, with respect to the
primary, as before (the only position which I had taken

* The reader is assumed to be already acquainted with the papers referred to.

INTRODUCTION

Fig. 1.

into consideration), and expected that when the block was
in place very strong sparks would appear in the secondary,
and that when the block was re-
moved there would only be feeble
sparks. This latter expectation
•was based upon the supposition
that the electrostatic forces could
in no case induce a spark in the
almost closed circuit C, for since "
these forces have a potential, it
follows that their integral over a
nearly closed circuit is vanishingly
small. Thus in the absence of the
insulator we should only have to
consider the inductive eflfect of the
more distant wire a 6. The experiment was frustrated by the
invariable occurrence of strong sparking in the secondary
conductor, so that the moderate strengthening or weakening
effect which the insulator must exert did not make itself
felt. It only gradually became clear to me that the
law which I had assumed as the basis of my experiment
did not apply here; that on account of the rapidity of the
motion even forces which possess a potential are able to in-
duce sparks in the nearly closed conductor ; and, in general,
that the greatest care has to be observed in applying here
the general ideas and laws which form the basis of the
usual electrical theories. These laws all relate to statical or
stationary states ; whereas here I had truly before me a vari-
able state. I perceived that I had in a sense attacked the
problem too directly. There was yet an infinite number of
other positions of the secondary with respect to the primary
conductor, and among these there might well be some more
favourable for my purpose. These various positions had first
to be examined. Thus I came to discover the phenomena
which are described in the fifth paper ("On the Action of a
Eectilinear Electric Oscillation upon a Neighbouring Circuit^'),
and which surprised me by their variety and regularity. The
finding out and unravelling of these extremely orderly pheno-
mena gave me peculiar pleasure. The paper certainly does
not include all the discoverable details; whoever may extend

6 INTRODUCTION I

the experiments to various other forms of conductor will find
that the task is not an ungrateful one. The observations at
greater distances are also probably very inaccurate, for they
are affected by the disturbing influence of reflections which
were not at that time suspected. What especially surprised
me was the continual increase of the distance up to which I •
could perceive the action ; up to that time the common view
was that electric forces decreased according to the Newtonian
law, and therefore rapidly tended to zero as the distance
increased.

Now during the course of this investigation I had made
sure of other positions of the secondary conductor in which
it was possible, by bringing an insulator near, to cause the
appearance or disappearance of sparks, instead of simply
altering their size. The problem which I was investigating
was now solved directly in the manner described in the sixth
paper (" On Electromagnetic Effects produced by Electrical
Disturbances in Insulators"). On 10th November 1887 I
was able to report the successful issue of the work to the
Berlin Academy.

The particular problem of the Academy which had been
my guide thus far was evidently propounded at the time by
Herr von Helmholtz in the following connection: — If we
start from the electromagnetic laws which in 1879 enjoyed
universal recognition, and make certain further assumptions,
we arrive at the equations of Maxwell's theory which at that
time (in Germany) were by no means universally recognised.
These assumptions are : first, that changes of dielectric polar-
isation in non-conductors produce the same electromagnetic
forces as do the currents which are equivalent to them ;
secondly, that electromagnetic forces as well as electrostatic
are able to produce dielectric polarisations ; thirdly, that in all
these respects air and empty space behave like all other
dielectrics. In the latter part of his paper (" On the Equations \

of Motion of Electricity for conducting Bodies at Eest"),^ von
Helmholtz has deduced Maxwell's equations from the older
views and from hypotheses which are equivalent to those
just stated. The problem of proving all three hypotheses,
and thereby establishing the correctness of the whole of

^ V. Helmholtz, Ges, AhhandL 1, p. 545.

I INTRODUCTION 7

Maxwell's theory, appeared to be an unreasonable demand ;
the Academy, therefore, contented itself with requiring a
confirmation of one of the first two.

The first assumption was now shown to be correct I
thought for some time of attacking the second. To test it
appeared by no means impossible ; and for this purpose I cast
closed rings of paraffin. But while I was at work it struck me
that the centre of interest in tlie new theory did not lie in the
consequences of the first two hypotheses. If it were shown that
these were correct for any given insulator, it would follow that
waves of the kind expected by Maxwell could be propagated
in this insulator, with a finite velocity which might perhaps
differ widely from that of light I felt that the third hypo-
thesis contained the gist and special significance of Faraday's,
and therefore of Maxwell's, view, and that it would thus be a
more worthy goal for me to aim at I saw no way of testing
separately the first and the second hypotheses for air ; ^ but
both hypotheses would be proved simultaneously if one could
succeed in demonstrating in air a finite rate of propagation
and waves. Certainly some of the first experiments in this
direction failed; these are described in the paper referred to,
and they were carried out at short distances. But in the
meantime I had succeeded in detecting the inductive action
at distances up to 12 metres. Within this distance the
phase of the motion must have been reversed more than
once; and now it only remained to detect and prove
this reversal. Thus the scheme was conceived which was
carried out as described in the research " On the Finite
Velocity of Propagation of Electromagnetic Actions." The first
step that had to be taken was easy. In straight stretched
wires surprisingly distinct stationary waves were produced
with nodes and antinodes, and by means of these it was
possible to determine the wave-length and the change of phase
along the wire. Nor was there any greater difficulty in pro-
ducing interference between the action which had travelled
along the wire and that which had travelled through the air,
and thus in comparing their phases. Now if both actions

^ The expressions air (Luftraum) and empty space {leerer Baum) are here
used as synonymous, inasmuch as the influence of the air itself in these experi-
ments is negligible.

8 INTRODUCTION I

were propagated, as I expected, with one and the same finite
velocity, they must at all distances interfere with the same
phase. ^ A simple qualitative experiment which, with the
experience I had now . gained, could be finished within an 1

hour, must decide this question and lead at once to the goal.
But when I had carefully set up the apparatus and carried
out the experiment, I found that the phase of the interference
was obviously different at different distances, and that the
alternation was such as would correspond to an infinite rate
of propagation in air. Disheartened, I gave up experimenting.
Some weeks passed before I began again. I reflected that it
would be quite as important to find out that electric force was
propagated with an infinite velocity, and that Maxwell's theory
was false, as it would be, on the other hand, to prove that
this theory was correct, provided only that the result arrived ^

at should be definite and certain. I therefore confirmed with ^

the greatest care, and without heeding what the outcome might
be, the phenomena observed : the conclusions arrived at are
given in the paper. When I then proceeded to consider more
closely these results, I saw that the sequence of the inter-
ferences could not be harmonised with the assumption of an
infinite rate of propagation ; that it was necessary to assume
that the velocity was finite, but greater than that in the wire.
As shown in the paper, I endeavoured to bring into harmony
the various possibilities ; and although the difference in the |

velocities appeared to me to be somewhat improbable, I could
see no reason for mistrusting the experiments. And it was
not by any means impossible that the motion in the wire |

might be retarded by some unknown causes, as, for example, by ^

an essential inertia of the free electricity. |

I have entered into these details here in order that
the reader may be convinced that my desire has not been
simply to establish a preconceived idea in the most convenient
way by a suitable interpretation of the experiments. On the
contrary, I have carried out with the greatest possible care
these experiments (by no means easy ones), although they
were in opposition to my preconceived views. And yet,
although I may have been lucky elsewhere, in this research I
have been decidedly unlucky. For instead of reaching the
right goal with little effort, as a properly devised plan might

I INTRODUCTION 9

have enabled me to do, I seem to have taken great pains, and
to have fallen into error after alL

In the first place, the research is disfigured by an error of
calculation. The time of oscillation is overestimated in the

ratio of v2 : 1. M. Poincar^ first drew attention to this
error.^ As a matter of fact, this error affects the form of the
research more than the substance of it. My reliance on the
correctness of the calculation was mainly due to its supposed
accordance with the experiments of Siemens and Fizeau and
^th my own.^ If I had used the correct value for the
capacity, and so found out the discrepancy between calculation
and experiment, I would have placed less reliance on the
calculation; the investigation would have been somewhat
altered in form, but the subject-matter would have remained
unaltered.

In the second place (and this is the more important point),
one of the principal conclusions of the investigation can
scarcely be regarded as correct — namely, that the velocities in
air and in the wire are different Such further knowledge as
has been gained respecting waves in wires, instead of confirm-
ing this result, tends to make it more and more improbable.
It now seems fairly certain that if the experiment had been
carried out quite correctly, and without any disturbing causes,
it would have given almost exactly the result which I expected
at the start. There is no doubt that the' phase of the inter-
ference must have changed sign once (and this I had not
expected beforehand) ; but the interference should have ex-
hibited no second change of sign ; and yet the experiments
without exception pointed to this. It is not easy to point to
any disturbing cause which could imitate in such a deceptive
way the effect of a difference in velocity; but there is no
reason why we should not admit the possibility of such a
deception. While performing the experiments, I never in the
least suspected that they might be affected by the neighbour-
ing walls. I remember that the wire along which the waves
travelled was carried past an iron stove, and only 1*5 metres
from it. A disturbance caused in this way, and always acting
at the same point, might have given rise to the second change

^ H. Poincare, Comptes EenduSf 111, p. 322.
^ See the remark at the end of the second part of the paper (p. 114).

10 INTRODUCTION i

of phase of the iuterference. However this may be, I should
like to express a hope that these experiments may be repeated
by some other observer under the most favourable conditions
possible, i.e. in a room as large as possible. If the plan of
the experiment is correct, as I think it is, then it must, when-
ever properly carried out, give the result which it should at
first have given ; it would then prove without measurement
the finite velocity of propagation of the waves in air, and at
the same time the equality between this and the velocity of
the waves in the wire.

I might also mention here some further considerations which
at that time strengthened mv conviction that the waves in the
wire suffered a retardation. If the waves in the wire run along
at the same speed as waves in air, then the lines of electric
forces must be perpendicular to the wire. Thus a straight
wire traversed by waves cannot exert any inductive action
upon a neighbouring parallel wire. But I found that there
was such an action, even though it was only a weak one. I
concluded that the lines of force were not parallel to the wire,
and that the velocity of the waves was not the same as that
of light. Further, if the lines of force are perpendicular to
the wire, it can be shown by a simple calculation that the
energy propagated by a wave in a single wire becomes log-
arithmically infinite. I therefore concluded that such a wave
was d priori impossible. Lastly, it seemed to me that it could
have no effect upon the rate of propagation in a straight con-
ductor, whether that conductor was a smooth wire or a wire
with side projections, or a crooked wire, or a spiral wire with
small convolutions, provided always that these deviations from
the straight line were small compared with the wave-length,
and that their resistance did not come into consideration.
But now I found that all these alterations produced a very
noticeable efi'ect upon the velocity. Hence I concluded that
here again there was some obscure cause at work which caused
a retardation, and which would also make itself felt in simple
smooth wires. At the present moment these and other
reasons do not appear to me to be of decisive weight ; but at
that time they so far satisfied me that I asserted without any
reserve that there was a difference between the velocities, and
regarded this decision as one of the most interesting of my

I INTRODUCTION 1 1

experimental results. Soon I was to discover what appeared
to be a confirmation of my opinion ; and at that time it was
very welcoma

While investigating the action of my primary oscillation
at great distances, I came across something like a formation of
shadows behind conducting masses, and this did not strike me
as being very surprising. Somewhat later on I thought that
I noticed a peculiar reinforcement of the action in front of
such shadow-forming masses, and of the walls of the room.
At first it occurred to me that this reinforcement might
arise from a kind of reflection of the electric force from
the conducting masses; but although I was familiar with
the conceptions of Maxwell's theory, this idea appeared
to me to be almost inadmissible — so utterly was it at
variance with the conceptions then current as to the nature
of an electric force. But when I had established with
certainty the existence of actual waves, I returned to the
mode of explanation which I had at first abandoned, and so*
arrived at the phenomena which are described in the paper
" On Electromagnetic Waves in Air, and their Eeflection." No
objection can be urged against the qualitative part of this
research — the experiments have been frequently repeated and
confirmed. But the part 'of the research which relates to
the measurements is doubtful, inasmuch as it also leads to
the very unlikely result that the velocity in air is considerably
greater than that of waves in wires. Assuming that this
result is incorrect, how are we to explain the error which has
crept in ? Certainly it is not due to simple inaccuracy of
observation. The error of observation may perhaps be about
a decimetre, but certainly not a metre. I can only here
attribute the mistake in a general sense to the special con-
ditions of resonance of the room used. The vibrations natural
to it may possibly have been aroused, and I may have ob-
served the nodes of such a vibration when I thought that I
was observing the nodes of the waves of the primary con-
ductor. There was certainly a substantial difference between
the distances of the nodes in air which I measured and the
wave-lengths in the wire. I specially directed my attention
to the question whether or not such a difference existed. As
far as any exact accordance with the first series of experi-

12 INTRODUCTION i

meiits is concerned, I freely allow that in the interpretation of
the experimental results I may have allowed myself to be
influenced by a desire to establish an accordance between the
two sets of measurements. I put back the first node a cer-
tain distance behind the wall, and an exact control of the
amount of this cannot be deduced from the experiments. If
I had wished to combine the experiments otherwise, I might
indeed have been able to calculate a ratio of the velocities
which would come out nearer to unity; but I certainly could
not infer from them that the velocities were equal.

Now, if the experiments which I made at that time all
^gree in pointing to a difierence between the velocities, it will
naturally be asked what reasons now induce me to allow
that there may have been unknown sources of error in the
experiments, rather than to abide by the statement made as to
the difference of velocities. Is it the objection which has been
raised in several quarters as to the want of accord between
the results and the theory ? Certainly not. The theory was
known to me at the time ; and furthermore, it must be sub-
ordinated to the experiments. Is it the experiment in this
connection made by Herr Lecher ? ^ This, too, I must deny,
although I fully recognise the value of the work which Herr
Lecher has done in this direction. In working out his results
Herr Lecher assumes that the calculation is correct, and there-
fore in a certain sense that the theory itself is correct.^ Is it
then the results of MM. Sarasin and de la Eive,^ who carefully
repeated the experiments and arrived at conclusions which
were completely in accord with the theory ? In a certain
sense, yes ; in another sense, no. The Genevan physicists
worked in a much smaller room than my own ; the greatest
distance of which they could avail themselves was only 10
metres, and the waves could not develop quite freely even up to
this distance. Their mirror was only 2-8 metres high. Care in
carrying out the observations cannot compensate for the un-
favourable nature of the room. In my experiments, on the
other hand, the waves had perfectly free play up to 15

^ E. Lecher, "Eine Studie iiber elektrische ResonanzerscheiDungen," Wi^.
Ann. 41, p. 850.

'^ The same remark holds good for the work recently published by M.
Blondlot, C, R. 113, p. 628 (cjp. Note 15 at end of book).

' E. Sarasin and L. de la Kive, Comptes Rendus, 112, p. 658.

I INTRODUCTION 13

metres. My mirror was 4 metres high. If the decision
rested simply and solely with the experiments, I could not
attribute greater weight to those of MM. Sarasin and de la
Eive than to my own.^ So far, then, I again say no. But
certainly the Genevan experiments show that my experi-
ments are subject to local variations ; they show that the
phenomena are dififerent if the reflecting walls and the rooms
are different, and also that under certain conditions the
wave-lengths have the values required by theory. But if the
experiments furnish information which is ambiguous and con-
tradictory, they obviously contain sources of error which are
not understood ; and hence they cannot be brought forward as
arguments against a theory which is supported by so many
reasons based on probability. Thus the Genevan experiments
deprive my own of their force, and so far they restore the
balance of probability to the theoretical side.

Still, I must acknowledge that the reasons which decided
me were of a more indirect kind. When I first thought that
I had found a retardation of waves in the wires, I hoped soon
to discover the cause of this retardation, and to find some
gradual change in its value. This hope has not been
realised. I found no such change, and, as my experience
increased, instead of coming across an explanation, I met with
increasing discrepancies, until these at last appeared to me to
be insoluble, and I had to give up all hope of proving the
correctness of my first observation. My own discovery, that
for short waves the difference between the velocities very
nearly disappears, tended in the same direction. Before one
of my scientific colleagues had attacked this question, I had
stated my opinion in the following words '? — " Thus I found
that for long waves the wave-length is gteater in air than in
wires, whereas for short waves both appear to be practically
equal. This result is so surprising that we cannot regard it
as certain. The decision must be reserved until further ex-
periments are made." The only experiments of the kind
referred to that have hitherto been made are those of MM.
Sarasin and de la Eive ; and inasmuch as these were carried

^ Mr. Trouton, in a room of which the dimensions are not exactly given,
found, like myself, that the wave-length of my primary conductor in air was.
about 10 metres. — Naiurey 39, p. 391.

2 Archives de Geridve (3), 21, p. 302.

14 INTRODUCTION i

out in small rooms, they may more properly be regarded as a
confirmation of the second part of my statement than as a refut-
ation of the first part. Decisive experiments for long waves
seem to me to be still wanting.^ I have little doubt that they
will decide in favour of equal velocities in all cases.

The reader may, perhaps, ask why I have not endeavoured
to settle the doubtful point myself by repeating the experi-
ments. I have indeed repeated the experiments, but have only
found, as might be expected, that a simple repetition under
the same conditions cannot remove the doubt, but rather
increases it. 4- definite decision can only be arrived at by
experiments carried out under more favourable conditions.
More favourable conditions here mean larger rooms, and such
were not at my disposal. I again emphasise the statement
that care in making the observations cannot make up for want
of space. If the long waves cannot develop, they clearly
cannot be observed.

The experiments hitherto described on the reflection of waves
were finished in March 1888. In the same month I attempted,
by means of reflection at a curved surface, to prevent the
dispersion of the action. For my large oscillator I built a
concave parabolic mirror of 2 metres aperture and 4 metres
high. Contrary to my expectation I found that the action
was considerably weakened. The large mirror acted like a
protecting screen surrounding the oscillator. I concluded that
the wave-length of the oscillation was too large in comparison
with the focal length of the mirror. A moderate reduction in
the size of the primary conductor did not improve the result.
I therefore tried to work with a conductor which was geo-
metrically similar to the larger one, but smaller in the pro-
portion of 10 : It Perhaps I did not persevere sufficiently in
this attempt ; at any rate I entirely failed at that time to pro-

^^ Since the above was written, the wish expressed has been amply satisfied
by the experiments which MM. Sarasin and de la Rive have carried out in the
great hall of the Rhone waterworks at Geneva (see Archives de OerUve, 29, pp.
358 and 441). These experiments have proved the equality of the velocity in
air and in wires, and have thus established the full agreement between experi-
ment and theory. I consider these experiments to be conclusive, and submit to
them now with as much readiness as I then felt hesitation in submitting to
experiments which were not superior to my own. I gladly avail myself of the
opportunity of thanking MM. Sarasin and de la Rive lor the great kindness and
goodwill which they invariably exhibited in the whole controversy — a controversy
which has now been decided entirely in their own favour.

I INTRODUCTION 15

dace and observe such short oscillations, and I abandoned these
experiments in order to turn my attention to other questions.

In the first place, it was important to devise a clearer theo-
retical treatment of the experiments. In the researches to which
I have hitherto referred, the experiments were interpreted from
the standpoint which I took up through studying von Helm-
holtz's papers.^ In these papers Herr v. Helmholtz distinguishes
between two forms of electric force — the electromagnetic and
the electrostatic — to which, until the contrary is proved by
experience, two different velocities are attributed. An inter-
pretation of the experiments from this point of view could
certainly not be incorrect, but it might perhaps be unneces-
sarily complicated. In a special limiting case Helmholtz's
theory becomes considerably simplified, and its equations in
this case become the same as those of Maxwell's theory ; only
one form of the force remains, and this is propagated with
the velocity of light. I had to try whether the experiments
would not agree with these much simpler assumptions of
Maxwell's theory. The attempt was successful. The results
of the calculation are given in the paper on "The Forces of
Electric Oscillations, treated according to Maxwell's Theory."
That part of the research which relates to interference between
waves in air and in wires could clearly be adapted without
diflSculty to any other form of such interference which might
result from more complete experiments.

Side by side with the theoretical discussions I continued
the experimental work, directing the latter again more to waves
in wires. In doing so, my primary object was to find out
the cause of the supposed retardation of these waves.
Secondly, I wished to test the correctness of the view accord-
ing to which the seat and field of action, of the waves is not
in the interior of the conductor, but rather in the surrounding
space. I now made the waves travel in the interspace be-
tween two wires, between two plates, and in tubular spaces,
instead of along a single wire ; in various interposed insulators
instead of in different metals. The research on " The Propa-
gation of Electric Waves by Means of Wires " was, for the
most part, carried out in the summer of 1888, although it
was only completed and published later on.

^ V. Helmholtz, Ges. AbhandL 1, p. 545.

^ OFTHE '^

UNIVERSITr

16 INTEODUCT.ON I

For in the autumn a singular phenomenon attracted my
attention away from the experiments with wires. For the
investigation of waves in the narrow interspace between two
wires I was using resonators of small external dimensions, and
was engaged in tuning these. I found that I obtained distinct
nodes at the end of the wires even when I used resonators
which were much too smalL Even when I diminished the
size of the circles to a few centimetres diameter, I still obtained
nodes ; these were situated at a small distance from the end of
the wires, and I could observe half wave-lengths as small as
12 cm. Thus chance brought me on to the track, hitherto
undiscovered, of the short waves. I at once followed up this
track, and soon succeeded in finding a form of the primary
conductor which could be used with the small resonators.

I paid no special attention to the phenomenon which led
me back to the observation of short waves ; and, as no suitable
occasion arose for doing so, I have not mentioned it in my
papers. Clearly it was a special case of the same phenomenon
which was later on discovered by MM. Sarasin and de la
Eive,^ called by the name of " Multiple Eesonance," and ex-
plained by saying that the primary conductor did not possess
any definite period of oscillation, but that it performed simul-
taneously all possible oscillations lying within wide limits. If
I paid little attention myself to this phenomenon, it was
partly because I was soon led on to other researches. It
arose no less from the fact that I had from the start
conceived an interpretation of the phenomenon which lent
much less interest to it than the interpretation given by
MM. Sarasin and de la Eive. I regarded the phenomenon
as a consequence of the rapid damping of the primary
oscillation — a necessary consequence, and one which could
be foreseen. M. Sarasin was good enough to communicate
at once to me the results of his research, and I told him my
doubts as to his explanation of the phenomenon, and gave
him my own explanation of it ; but although he received my
explanation with the readiest goodwill, we did not succeed in
coming to a common understanding as to the interpretation of
the experiment. With M. H. Poincar^ such an understanding
was secured at once; he had formed a conception of the

^ E. Sarasin and L. de la Rive, Arch, de GerUve (3), 23, p. 113, 1890.

I INTEODUCnON 17

phenomenon which was practically identical with my own,
and had communicated it to me in a letter. This conception
he has worked out mathematically, and published in his book
ElectridU et Optigue} Herr V. Bjerknes has worked out the
mathematical developments simultaneously and independently.^
That the explanation given by MM. Poincar^ and Bjerknes is
not only a possible one, but is the only possible one, appears to
me to be proved by an investigation by Herr Bjerknes,* which
has appeared recently, and which makes it certain that the
vibration of the primary conductor is, at any rate to a first
approximation, a uniformly damped sine- wave of determinate
period. Hence the careful investigations of MM. Sarasin and
de la Eive are of great value in completing our knowledge of
this part of the work, but they in no way contradict any
statement made by me. The authors themselves regard their
experiments in this light. Nevertheless, these experiments
gave occasion to an adverse criticism of my work from a
distinguished French physicist who had not, however, repeated
the experiments himself. I hope it will now be allowed that
there was no cause for such a criticism.*

I may be permitted to take this opportunity of referring
to the doubts which have recently been raised by Herm
Hagenbach and Zehnder as to what my experiments really
prove.^ Perhaps I ought not yet to consider their work as
being completed. The authors reserve to themselves the right
of returning to the explanation of resonance and the formation
of nodes and antinodes in my experiments. But it is just
precisely upon these phenomena that my experiments, and
the whole interpretation of them, rest.

After I had succeeded (as already described) in observing
very short waves, I chose waves about 30 cm. long, and
repeated first of all the earlier experiments with these. I
now found, contrary to my expectation, that these short waves
travelled along wires with very nearly the same velocity as in
air. As it was easy to procure free play for such short waves,
no doubt could arise in this case as to the correctness of the

^ H. Poincare, Electricity et Optique, 2, p. 249.
2 V. Bjerknes, Wied. Ann. 44, p. 92, 1891.
* Ibid. 46, p. 513, 1891.
* Cornu, Comptes Rendiis, 110, p. 72, 1890.
^ E. Hagenbach and L. Zehnder, Wied. Ann. 43, p. 610, 1891.

18 UTTRODUCTION i

results. After I had become quite used to managing these
short waves, I returned to the experiment with the concave
reflector. The large old reflector was no longer at my dis-
posal, so I had a smaller one made, about 2 metres high and a
little more than 1 metre in aperture. It worked so remark-
ably well that, directly after the first trial, I ordered not only
a second concave reflector, but also a plane reflecting surface
and a large prism. The experiments which are described
in the paper " On Electric Badiation " now followed each
other in rapid succession, and without difl&culty; they had
been considered and prepared long beforehand, with the excep-
tion of the polarisation-experiments, which only occurred to
me during the progress of the work. These experiments
with concave mirrors soon attracted attention ; they have fre-
quently been repeated and confirmed. The approval with
which they have been received has far exceeded my expecta-
tion.^ A considerable part of this approval was due to reasons
of a philosophic nature. The old question 'as to the possibility
and nature of forces acting at a distance was again raised. The
preponderance of such forces in theory has long been sanctioned
by science, but has always been accepted with reluctance by
ordinary common sense; in the domain of electricity these
forces now appeared to be dethroned from their position by
simple and striking experiments.

Though in the last-mentioned experiments my research had,
in a certain sense, come to its natural end, I still felt that there
was one thing wanting. The experiments related only to the
propagation of the electric force. It was desirable to show that
the magnetic force was also propagated with a finite velocity.
According to theory it was not necessary for this purpose to
produce special magnetic waves ; the electric waves should at
the same time be waves of magnetic force ; the only important
thing was to really detect in these waves the magnetic force
in the presence of the electric fof ce. I hoped that it would be
possible to do this by observing the mechanical forces which
the waves exerted upon ring-shaped conductors. So experi-
ments were planned which (for other reasons) were only

^ These experiments gave occasion to the lecture ** On the Relations between
Light and Electricity," which I delivered to the NcUur/orscherversammlung at
Heidelberg in 1889, and in which I gave a general account of my experiments
in a popular form (published by E. Strauss, Bonn).

I INTRODUCTION 19

carried out later on, and then incompletely ; these are described
in the last experimental research " On the Mechanical Action
of Electric Waves in Wires."

Casting now a glance backwards we see that by the
experiments above sketched the propagation in time of a
supposed action-at-a-distance is for the first time proved.
This fact forms the philosophic result of the experiments ; and,
indeed, in a certain sense the most important result The
proof includes a recognition of the fact that the electric forces
can disentangle themselves from material bodies, and can con-
tinue to subsist as conditions or changes in the state of space.
The details of the experiments further prove that the particular
manner in which the electric force is propagated exhibits the
closest analogy ^ with the propagation of light ; indeed, that it
corresponds almost completely to it The hypothesis that
light is an electrical phenomenon is thus made highly probable.
To give a strict proof of this hypothesis would logically require
experiments upon light itself.

What we here indicate as having been accomplished by
the experiments is accomplished independently of the correct-
ness of particular theories. Nevertheless, there is an obvious
connection between the experiments and the theory in con-
nection with which they were really undertaken. Since the
year 1861 science has been in possession of a theory which
Maxwell constructed upon Faraday's views, and which we
therefore call the Faraday-Maxwell theory. This theory afiirms
the possibility of the class of phenomena here discovered just as
positively as the remaining electrical theories are compelled to
deny it From the outset Maxwell's theory excelled all others
in elegance and in the ^abundance of the relations between
the various phenomena which it included. The probability of
this theory, and therefore the number of its adherents, increased
from year to year. But as long as Maxwell's theory depended
solely upon the probability of its results, and not on the
certainty of its hypotheses, it could not completely displace
the theories which were opposed to it The fundamental
hypotheses of Maxwell's theory contradicted the usual views,

^ The analogy does not consist only in the agreement between the more or less
accurately measured velocities. The. approximately equal velocity is only one
element among many others.

20 INTEODUCTION i

and did not rest upon the evidence of decisive experiments.
In this connection we can best characterise the object and
the result of our experiments by saying : The object of these
experiments was to test the fundamental hypotheses of
the Faraday -Maxwell theory, and the result of the experi-
ments is to confirm the fundamental hypotheses of the theory.

B, Theoretical

And now, to be more precise, what is it that we call the
Faraday-Maxwell theory ? Maxwell has left us as the result
of his mature thought a great treatise on Electricity and
Magnetism ; it might therefore be said that Maxwell's theory is
the one which is propounded in that work But such an
answer will scarcely be regarded as satisfactory by all scientific
men who have considered the question closely. Many a man
has thrown himself with zeal into the study of Maxwell's
work, and, even when he has not stumbled upon unwonted
mathematical difficulties, has nevertheless been compelled to
abandon the hope of forming for himself an altogether con-
sistent conception of Ma^fwell's ideas. I have fared no better
myself. Notwithstanding the greatest admiration for Maxwell's
mathematical conceptions, I have not always felt quite certain
of having grasped the physical significance of his statements.
Hence it was not possible for me to be guided in my experi-
ments directly by Maxwell's book. I have rather been guided
by Helmholtz*s work, as indeed may plainly be seen from the
manner in which the experiments are set forth. But un-
fortunately, in the special Umiting case of Helmholtz's theory
which leads to Maxwell's equations, and to which the experi-
ments pointed, the physical basis of Helmholtz's theory dis-
appears, as indeed it always does, as soon as action-at-a-distance
is disregarded. I therefore endeavoured to form for myself in
a consistent manner the necessary physical conceptions, starting
from Maxwell's equations, but otherwise simplifying Maxwell's
theory as far as possible by eliminating or simply leaving out
of consideration those portions which could be dispensed with.

I INTKODUCTION 21

inasmuch as they could not affect any possible phenomena.
This explains how the two theoretical papers (forming the
conclusion of this collection) came to be written. Thus
the representation of the theory in Maxwell's own work,
its representation as a limiting case of Helmholtz's theory,
and its representation in- the present dissertations — ^however
different in form — ^have substantially the same inner significance.
This common significance of the different modes of represent-
ation (and others can certainly be found) appears to me to be
the undying part of Maxwell's work. This, and not Maxwell's
peculiar conceptions or methods, would I designate as " Max-
well's Theory." To the question, " What is Maxwell's theory ? "
I know of no shorter or more definite answer than the foUow-i
ing: — Maxwell's theory is Maxwell's system of equations.!
Every theory which leads to the same system of equations, and
therefore comprises the same possible phenomena, I would
consider as being a form or special case of Maxwell's theory ;
every theory which leads to different equations, and therefore
to different possible phenomena, is a different theory^ Hence
in this sense, and in this sense only, may the two theoretical
dissertations in the present volume be regarded as representations
of Maxwell's theory. In no sense can they claim to be a precise
rendering of Maxwell's ideas. On the contrary, it is doubtful
whether Maxwell, were he alive, would acknowledge them as
representing his own views in all respects.

The very fact that different modes of representation con-
tain what is substantially the same thing, renders the proper
understanding of any one of them all the more difficult. Ideas
and conceptions which are akin and yet different may be
s)nnbolised in the same way in the different modes of repre-
sentation. Hence for a proper comprehension of any one of
these, the first essential is that we should endeavour to under-
stand each representation by itself without introducing into it
the ideas which belong to another. Perhaps it may be of
service to many of my colleagues if I here briefly explain the
fundamental conceptions of the three representations of Max-
well's theory to which I have already referred. I shall thus
have an opportunity of stating wherein lies, in my opinion,
the especial difficulty of Maxwell's own representation. I can-

22 INTKODUCTION i

not agree with the oft-stated opinion that this difl&culty is of
a mathematical nature.

When we see bodies acting upon one another at a distance,
we can form for ourselves various conceptions of the nature of
this action. We may regard the effect as being that of a
direct action-at-a-distance, springing across space, or we may
regard it as the consequence of an action which is propagated
from point to point in a hypothetical medium. Meanwhile,
in applying these conceptions to electricity, we can make a
series of finer distinctions. As we pass from the pure conception
of direct attraction to the pure conception of indirect (ver-
mittelten) attraction, we can distinguish between four stand-
points.

From the first standpoint we regard the attraction of two
bodies as a kind of spiritual afl&nity between them. The force
which each of the two exerts is bound up with the presence of
the other body. In order that force should be present at all,
there must be at least two bodies present. In some way a
magnet only obtains its force when another magnet is brought
into its neighbourhood. This conception is the pure con-
ception of action-at-a-distance, the conception of Coulomb's
law. In the theory of electricity it has almost been aban-
doned, but it is still used in the theory of gravitation. Mathe-
matical astronomy speaks of the attraction between the sun
and a planet, but with attraction in empty space it has no
concern.

From the second standpoint we still regard the attraction
of the bodies as a kind of spiritual influence of each upon the
other. But although we admit that we can only notice this
action when we have at least two bodies, we further assume
that each of the acting bodies continually strives to excite at
all surrounding points attractions of definite magnitude and
direction, even if no other similar bodies happen to be in the
neighbourhood. With these strivings, varying always from
point to point, we fill (according to this conception) the surround-
ing space. At the same time we do not assume that there is
any change at the place where the action is exerted ; the acting
body is still both the seat and the source of the force. This
is about the standpoint of the potential theory. It obviously

INTKODUCTION

•r

^////A

postUv JDUetricUajL
TtsffcUintJZeetricitat,

Fig. 2. [II.]

is also the standpoint of certain chapters in Maxwell's work,
although it is not the standpoint of Maxwell's theory. In
order to compare these con-
ceptions more easily with one
another, we represent from this
standpoint (as in Fig. 2) two
oppositely electrified condenser-
plates. The diagrammatic
representation will be easily
understood; upon the plates
are seen the positive and
negative electricities (as if
they were material) ; the force
between the plates is indicated
by arrow& From this standpoint it is immaterial whether the
space between the plates is full or empty. If we admit the
existence of the light-ether, but suppose that it is removed from
a part B of the space, the force will still remain unaltered in
this space.

The third standpoint retains the conceptions of the second,
but adds to them a further complication. It assumes that the
action of the two separate bodies is not determined solely by
forces acting directly at a distance. It rather assumes that the
forces induce changes in the space (supposed to be nowhere
empty), and that these again give rise to new distance-forces
(FemJcrdften). The attractions between the separate bodies de-
pend, then, partly upon their direct action, and partly upon the
influence of the changes in the medium. The change in the
medium itself is regarded as an electric or magnetic polarisa-
tion of its smallest parts under the influence of the acting
force^I This view has been developed by Poisson with respect
to statical phenomena in magnetism, and has been transferred
by Mosotti to electrical phenomena. In its most general
development, and in its extension over the whole domain of
electromagnetism, it is represented by Helmholtz's theory.^

Fig. 3 illustrates this standpoint for the case in which
the medium plays only a small part in the resultant action.
Upon the plates are seen the free electricities, and in the parts

^ At the end of the paper ** On the Equations of Motion of Electricity for
Conducting Bodies at Rest. " — Ges. Ahh. 1, p. 545.

INTRODUCTION

Fig. 8. [Ilia.]

of the dielectric the electrical fluids which are separated, but
which cannot be divorced from each other. Let us suppose that

the space between the plates
contains only the light -ether,
and let a space, such as B, be
hollowed out of this ; the forces
— will then remain in this space,
but the polarisation will dis-
appear.

One limiting case of this
mode of conception is of
especial importance. As closer
examination shows, we can split up the resultant action (which
alone can be observed) of material bodies upon one another into
an influence due to direct action-at-a-distance, and an influence
due to the intervening medium. We can increase that part of
the total energy which has its seat in the electrified bodies at the
expense of that part which we seek in the medium, and con-
versely. Now in the limiting case we *seek the whole of the
energy in the medium. Since no energy corresponds to the
electricities which exist upon the conductors, the distance-forces
must become infinitely small. But for this it is a necessary
condition that no free electricity should be present. The
electricity must therefore behave itself like an incompressible
fluid. Hence we have only closed currents ; and hence arises
the possibility of extending the theory to all kinds of electrical
disturbances in spite of our ignorance of the laws of unclosed
currents.

The mathematical treatment of this limiting case leads us
to Maxwell's equations. We tlierefore call this treatment a
form of Maxwell's theory. The limiting case is so called also
by V. Helmholtz. But in no sense must this be taken as
meaning that the physical ideas on which it is based are
Maxwell's ideas.

Fig. 4 indicates the state of the space between two
electrified plates in accordance with the conceptions of this
theory. The distance -forces have become merely nominal.
The electricity on the conductors is still present, and is a
necessary part of the conception, but its action-at-a-distance is

I INTEODUCnOH 25

completely neutralised by the opposite electricity of the
medium which is displaced to'wards it The pressure vhicb

this medium exerts, on account

of the attraction of its internal

electrifications, tends to draw the

plates together. In the empty

space B there are present only -i. —

vanishingly smfdl distance-forces.

The fourth standpoint be-
longs to the pure conception of
action through a medium. From
this standpoint we acknowledge "'

that the changes in space assumed from the third stand-
point are actually present, and that it ia by means of them
that material bodies act upon one another. But we do not
admit that these polarisations are the result of distance-forces ;
indeed, we altogether deny the existence of these distance-
forces ; and we discard the electricities from which these
forces are supposed to proceed. We now rather regard the
polarisations as the only things which are really present ;
they are the cause of the movements of ponderable bodies, and
of all the phenomena which allow of our perceiving changes
in these bodies. The explanation of the nature of the
polarisations, of their relations and effects, we defer, or else
seek to find out by mechanical hypotheses ; but we deelioe to
recognise in the electricities and distance-forces which have
hitherto passed current a satisfactory explanation of these
relations and effects. The expressions electricity, magnetism,
etc., have no further value for us beyond that of abbreviations.

Considered from the mathematical point of view, this
fourth mode of treatment may be regarded aa coinciding
completely with the limiting case of the third. But from
the physical point of view the two difi'er fundamentally. It
is impossible to deny the existence of distance -forces, and at
the same time to regard them as the cause of the polarisations.
Whatever we may designate as "electricity" from this stand-
point does not behave like an incompressible fluid. If we
consider Fig. 5, which brings symbolically before us the view
presented from this standpoint, we are struck by another dis-
tinction. The polarisation of the apace is represented by the

INTKODUCTION

Pig. 5. [IV.]

same symbolic method as was employed in discussing the
third standpoint. But whereas in Figs. 3 and 4 this mode
of representation explained the nature of the polarisation

through the nature of electri-
city (assumed to be known), we
have here to regard the mode of
representation as defining the
— nature of an electric charge
through the state of polarisa-
tion of the space (regarded as
known). Each particle of the
dielectric here appears charged
in opposite senses with elec-
tricity, just as it did from our third standpoint. If we again
remove the ether from the space B, there remains nothing
whatsoever in this space which could remind us of the elec-
trical disturbance in the neighbourhood.

Now this fourth standpoint, in my opinion, is Maxwell's
standpoint. The general explanations in his work leave
no room for doubting that he wished to discard distance-
forces entirely. He expressly says that if the force or
" displacement" in a dielectric is directed towards the right
hand, we must conceive each particle of the dielectric as
being charged with negative electricity on the right-hand
side, and with positive electricity on the left-hand side. But
it cannot be denied that other statements made by Maxwell
appear at first sight to contradict the conceptions of this
standpoint Maxwell assumes that electricity also exists in
conductors ; and that this electricity always moves in such a
way as to form closed currents with the displacements in the
dielectric. The statement that electricity moves like an incom-
pressible fluid is a favourite statement of Maxwell's. But these
statements do not fit in with the conceptions of the fourth
standpoint; they lead one to suspect that Maxwell rather
viewed things from the third point of view. My own opinion is
that this was never really the case ; that the contradictions are
only apparent and arise from a misunderstanding as to words.

The following, if I am not mistaken, is the state of affairs : —
Maxwell originally developed his theory with the aid of very
definite and special conceptions as to the nature of electrical

INTRODUCTIONS^ Oai .2\^...x > 27

phenomena. He assumed that the pores of the ether and of
all bodies were filled with an attenuated fluid, which, how-
ever, could not exert forces at a distance. In conductors this
fluid moved freely, and its motion formed what we call an
electric current. In insulators this fluid was confined to its
place by elastic forces, and its " displacement " was regarded as
being identical with dectric polar^ation. The fluid itself, as
being the cause of all electric phenomena, Maxwell called
"electricity." Now, when Maxwell composed his great treatise,
the accumulated hypotheses of this earlier mode of conception
no longer suited him, or else he discovered contradictions in
them, and so abandoned them. But he did not eliminate
them completely; quite a number of expressions remained
which were derived from his earUer ideas. And so, unfor-
tunately, the word " electricity," in Maxwell's work, obviously
has a double meaning. In the first place, he uses it (as we
also do) to denote a quantity which can be either positive or
negative, and which forms the starting-point of distance-forces
(or what appear to be such). In the second place, it denotes
that hypothetical fluid from which no distance-forces (not even
apparent ones) can proceed, and the amount of which in any
given space must, under all circumstances, be a positive
quantity. If we read Maxwell's explanations and always
interpret the meaning of the word " electricity " in a suitable
way, nearly all the contradictions which at first are so sur-
prising can be made to disappear. Nevertheless, I must
admit that I have not succeeded in doing this completely, or
to my entire satisfaction; otherwise, instead of hesitating, I
would speak more definitely.^

Whether this is so or not, an attempt has been made, in
the two theoretical papers here printed, to exhibit Maxwell's
theory, i.e. Maxwell's system of equations, from this fourth
standpoint. I have endeavoured to avoid from the beginning
the introduction of any conceptions which are foreign to this
standpoint and which might afterwards have to be removed.^

^ M. Poincar6, in his treatise ** Electricite et Optique" (vol. i., Les Theories de
Maxwell)j expresses a similar opinion. Herr L. boltzmann, in his Vorlesungen
fiber MaxwelVa Theorie, appears like myself to aim at a consistent development
of Maxwell's system rather than an exact rendering of Maxwell's thoughts.
Bnt no definite opinion can be given, inasmuch as the work is not yet completed.

2 The, expression ** electric force" in these papers is only another name for a
state of polarisation of space. It would perhaps have been better, in order to

28 INTRODUCTION i

I have further endeavoured in the exposition to limit as far
as possible the number of those conceptions which are arbi-
trarily introduced by us, and only to admit such elements as
cannot be removed or altered without at the same time altering
possible experimental results. It is true, that in consequence
of these endeavours, the theory acquires a very abstract and
colourless appearance. It is not particularly pleasing to hear
general statements made about " directed changes of state,"
where we used to have placed before our eyes pictures of
electrified atoms. It is not particularly satisfactory to see equa-
tions set forth as direct results of observation and experiment,
where we used to get long mathematical deductions as apparent
proofs of them. Nevertheless, I believe that we cannot, without
deceiving ourselves, extract much more from known facts than
is asserted in the papers referred to. If we wish to lend more
colour to the theory, there is nothing to prevent us from sup-
plementing all this and aiding our powers of imagination by
concrete representations of the various conceptions as to the
nature of electric polarisation, the electric current, etc. But
scientific accuracy requires of us that we should in no wise con-
fuse the simple and homely figure, as it is presented to us by
nature, with the gay garment which we use to clothe it.
Of our own free will we can make no change whatever in the
form of the one, but the cut and colour of the other we can
choose as we please.

Such further remarks as I may wish to make on points of
detail will be found at the end of the book as supplementary
notes.

prevent misconceptions, if I had replaced it by another expression, such, for
example, as ** electric field-intensity," or *' elektrische iTiiensUdtf** y^hich. Herr E.
Cohn proposes in his paper, which refers to the same subject (" Zur Systematik
der Elektricitatslehre/' JFied, Ann. 40, p. 625, 1890).

ON VERY RAPID ELECTRIC OSCILLATIONS

{Wiedemann's AnnaJen, 31, p. 421, 1887.)

The electric oscillations of open induction-coils have a period
of vibration which is measured by ten-thousandths of a second.
The vibrations in the oscillatory discharges of Leyden jars,
such as were observed by Feddersen,^ follow each other about
a hundred times as rapidly. Theory admits the possibility of
oscillations even more rapid than these in open wire circuits
of good conductivity, provided that the ends are not loaded
with large capacities; but at the same time theory does
not enable us to decide whether such oscillations can be
actually excited on such a scale as to admit of their being
observed. Certain phenomena led me to expect that oscilla-
tions of the latter kind do really occur under certain conditions,
and that they are of such strength as to allow of their effects
being observed. Further experiments confirmed my expecta-
tion, and I propose to give here an account of the experiments
made and the phenomena observed.

The oscillations which are here dealt with are about a
hundred times as rapid as those observed by Feddersen. Their
period of oscillation — estimated, it is true, only by the aid of
theory — is of the order of a hundred-millionth of a second.
Hence, according to their period, these oscillations range them-
selves in a position intermediate between the acoustic oscilla-
tions of ponderable bodies and the light-oscillations of the
ether. In this, and in the possibility that a closer observa-

^ For the literature see Colley, Wied, Ann, 26, p. 432, 1886. (See also Note
1 at the end of this book.) ^

30 ON VERY RAPID ELECTRIC OSCILLATIONS ii

tion of them may be of service in the theory of electro-
dynamics, lies the interest which they present

Preliminary EocperiraeTits

If, in addition to the ordinary spark-gap of an induction-
coil, there be introduced in its discharging circuit a Eiess's
spark-micrometer, the poles of which are joined by a long
metallic shunt, the discharge follows the path across the
air-gap of the micrometer in preference to the path along the
metallic conductor, so long as the length of the air-gap does
not exceed a certain limit. This is already known, and the
construction of lightning-protectors for telegraph-lines is based
on this experimental fact. It might be expected that, if the
metallic shunt were only made short and of low resistance, the
sparks in the micrometer would then disappear. As a matter
of fact, the length of the sparks obtained does diminish with
the length of the shunt, but the sparks can scarcely be made
to disappear entirely under any circumstances. Even when
the two knobs of the micrometer are connected by a few
centimetres of thick copper wire sparks can still be observed,
although they are exceedingly short. This experiment shows
directly that at the instant when the discharge occurs
the potential along the circuit must vary in value by
hundreds of volts even in a few centimetres ; indirectly it
proves with what extraordinary rapidity the discharge takes
place.' For the difference of potential between the knobs of
the micrometer can only be regarded as an effect of self-
induction in the metallic shunt. The time in which the
potential of one of the knobs Is appreciably changed is of the
same order as the time in which such a change is transmitted
to the other knob through a short length of a good conductor.
The potential difference between the micrometer-knobs might
indeed be supposed to be determined by the resistance of the
shunt, the current-density during the discharge being possibly
large. But a closer examination of the (quantitative relations
shows that this supposition is inadmissible ; and the following
experimeiit shows independently that this conjecture cannot be
put forward. We again connect the knobs of the micrometer
by a -good metaUic conductor, say by a copper wire 2 mm. in

ON VEBY RAPID ELECTRIC OSCILLATIONS

diameter and 0*5 metre long, bent into rectangular form ; we
do not, however, introduce this into the discharging^circuit of the
induction-coil, but we simply place one pole of it in communi-
cation with any point of the discharging circuit by means of
a connecting wire. (Fig. 6 shows the arrangement of the
apparatus ; A represents diagrammatically the induction-coil, B
the discharger, and M the micrometer.) Thereupon we again
observe, while the induction-coil is working, a stream of sparks
in the micrometer which may, under suitable conditions, attain
a length of several millimetres. Now this experiment shows,
in the first place, that at the instant when the discharge takes
place violent electrical disturbances occur, not only in the
actual discharging-circuit, but also in all
conductors connected with it But, in the
second place, it shows more clearly than
the preceding experiment that these dis-
turbances run on so rapidly that even the
• time taken by electrical waves in rushing
through short n^etallic conductors becomes
of appreciable importance. For the experi-
ment can only be interpreted in the sense
that the change of potential proceeding from
the induction-coil reaches the knob 1 in an
appreciably shorter time than the knob 2.
The phenomenonmay well cause surprise when
we consider that, as far as we know, electric
waves in copper wires are propagated with a velocity which is
approximately the same as that of light. So it appeared to
me to be worth while to endeavour to determine what con-
ditions were most favourable for the production of brilliant
sparks in the micrometer. For the sake of brevity we shall
speak of these sparks as the side-sparks (in order to distin-
guish them from the discharge proper), and of the micrometer
discharging-circuit as the side-circuit {Nebmkreis).

First of all it became evident that powerful discharges are
necessary if side-sparkS of several millimetres in length are
desired. I therefore used in all the following experiments a
large Euhmkorflf coil, 52 cm. long and 20 cm. in diameter,
which was provided with a mercury interrupter and was
excited by six large Bunsen cells. Smaller induction-coils

i 2

Fig. 6.

32 ON VERY RAPID ELECTRIC OSCILLATIONS ii

gave the same qualitative results, but the side-sparks were
shorter, and it was therefore more difficult to observe differences
between them. The same held good when discharges from
Leyden jars or from batteries were used instead of the induc-
tion-coiL It further appeared that even when the same
apparatus was used a good deal depended upon the nature of
the exciting spark in the discharger (B). If this takes place
between two points, or between a point and a plate, it only-
gives rise to very weak side-sparks; discharges in rarefied
gases or through Geissler tubes were found to be equally
ineffective. The only kind of spark that proved satisfactory
was that between two knobs (spheres), and this must neither
be too long nor too short. If it is shorter than half a centi-
metre the side-sparks are weak, and if it is longer than 1^
cm. they disappear entirely.

In the following experiments I used, as being the most
suitable, sparks three-quarters of a centimetre long between
two brass knobs of 3 cm. diameter. Even these sparks were
not always equally efficient; the most insignificant details,
often without any apparent connection, resulted in useless
sparks appearing instead of active ones. After some practice
one can judge from the appearance and noise of the sparks
whether they are such as are able to excite side-sparks. The
active sparks are brilliant white, slightly jagged, and are
accompanied by a sharp crackling. That the spark in the
discharger is an essential condition of the production of shunt-
sparks is easily shown by drawing the discharger-knobs so far
apart that the distance between them exceeds the sparking
distance of the induction-coil ; every trace of the side-sparks
then disappears, although the differences of potential now
present are greater than before.

The length of the micrometer-circuit naturally has great
influence upon the length of the sparks in it. For the greater
this distance, the greater is the retardation which the electric
wave suffers between the time of its arrival at the one knob
and at the other. If the side-circuit is made very small, the
side -sparks become extremely short; but it is scarcely
possible to prepare a circuit in which sparks wiU not show
themselves under favourable circumstances. Thus, if you file
the ends of a stout copper wire, 4-6 cm. long, to sharp points,

II ON VERY RAPID ELECTRIC OSCILLATIONS 33

bend it into an almost closed circuit, insulate it and now touch
the discharger with this small wire circuit, a stream of very-
small sparks between the pointed ends generally accompanies
the discharges of the induction-coil. The thickness and
material (and therefore the resistance) of the side-circuit have
very little effect on the length of the side-sparks. We were
therefore justified in declining to attribute to the resistance the
differences of potential which arise.) And according to our
conception of the phenomenon, the fact that the resistance is
of scarcely any importance can cause us no surprise ; for, to a
first approximation, the rate of propagation of an electric wave
along a wire depends solely upon its capacity and self-induction,
and not upon its resistance. The length of the wire which
connects the side-circuit to the principal circuit has also little
effect, provided it does not exceed a few metres. We must
assume that the electric disturbance which proceeds from the
principal circuit travels along it without suffering any real
change of intensity.

On the other hand, the position of the point at which
contact with the side-circuit is made has a very noteworthy
effect upon the length of the sparks in it. We should expect
this to be so if our interpretation of the phenomenon is correct.
For if the point of contact is so placed that the paths from it
to the two knobs of the micrometer are of equal length, then
every variation which passes through the connecting wire will
arrive at the two knobs in the same phase, so that no differ-
ence of potential between them can arise. Experiment confirms
this supposition. Thus, if we shift the point of contact on the
side-circuit, which we have hitherto supposed near one of the
micrometer-knobs, farther and farther away from this, the
spark-length diminishes, and in a certain position the sparks
disappear completely or very nearly so ; they become stronger
again in proportion as the contact approaches the second
micrometer-knob, and in this position attain the same length
as in the first. The point at which the spark-length is a
minimum may be called the null-point. It can generally be
determined to within a few centimetres. It always divides
the length of the wire between the two micrometer-knobs into
very nearly equal parts. If the conductor is symmetrical on
the right and left of the line joining the micrometer and the

ON VEBT RAPID ELECTRIC OSCILLATIONS

S. 2

Fig 7.

null-poiut, the sparks always disappear completely, the
phenomenoii can be observed even with quite short side-
circuits. Fig. 7 shows a convenient arrangement of the ex-
periment ; a 6 c d is a rectangle of bare copper wire 2 mm. in

diameter, insulated upon sealing-wax sup-
ports; ^ in my experiments it was 80 cm.
broad and 125 long. When the connecting
_o wire is attached to either of the knobs 1
and 2, or either of the points a and 6,
sparks 3-4 mm. long pass between 1 and
2 ; no sparks can be obtained when the
connection is at the point e, as in the
figure ; shifting the contact a few centi-
metres to right or left causes the sparks
to reappear. It should be remarked that
we consider sparks as being perceptible
when they are only a few hundredths of a
miUimetre in length.

The following experiment shows that
the above is not a complete representation of the way in
which things go on. For if, after the contact has been
adjusted so as to make the sparks disappear, we attach to one
of the micrometer-knobs another conductor projecting beyond
it, active sparking again occurs. This conductor, being
beyond the knob, cannot affect the simultaneous arrival of
the waves travelling from e to 1 and 2. "But it is easy to see
what the explanation of this experiment is. The waves do
not come to an end after rushing once towards a and h ; they
are reflected and traverse the side -circuit several, perhaps
many, times and so give rise to stationary oscillations in it.
If the paths e c a 1 and e dh 2 are equal, the reflected waves
will again arrive at 1 and 2 simultaneously. If, however, the
wave reflected from one of the knobs is missing, as in the last
experiment, then, although the first disturbance proceeding
from e will not give rise to sparks, the reflected waves wiU.
We must therefore imagine the abrupt variation which arrives
at e as creating in the side-circuit the oscillations which are
natural to it, much as the blow of a hammer produces in an
elastic rod its natural vibrations. If this idea is correct, then

^ [See Note 2 at end of book.]

II ON VERY RAPID ELECTRIC OSCILLATIONS 35

the condition for disappearance of sparks in M must substan-
tially be equality of the vibration-periods of the two portions
e 1 and e 2. These vibration-periods are determined by the
product of the coefficient of self-induction of those parts of the
conductor into the capacity of their ends ; they are practically
independent of the resistance of the branches. The following
experiments may be applied to test these considerations and
are found to agree with them : —

If the connection is placed at the null-point and one of
the micrometer-knobs is touched with an insulated conductor,
sparking begins again because the capacity of the branch is
increased. An insulated sphere of 2-4 cm. diameter is quite
sufficient. The larger the capacity which is thus added, the
more energetic becomes the sparking. Touching at the null-
point has no influence since it affects both branches equally.
The effect of adding a capacity to one branch is annulled by
adding an equal capacity to the other. It can also be com-
pensated by shifting the connecting wire in the direction of the
loaded branch, i.e. by diminishing the self-induction of the
•latter. The addition of a capacity produces the same effect as
increasing the coefficient of self-induction. If one of the
branches be cut and a few centimetres or decimetres of coiled
copperwire introduced into it,sparking begins again. The change
thus produced can be compensated by inserting an equal length
of copper wire in the other branch, or by shifting the copper
wire towards the branch which was altered, or by adding a'
suitable capacity to the other branch. Nevertheless, it must
be remarked that when the two branches are not of like kind,
a complete disappearance of the sparks cannot generally be
secured, but only a minimum of the sparking distance.

The results are but little affected by the resistance of the
branch. If the thick copper wire in one of the branches was
replaced by a much thinner copper wire or by a wire of Ger-
man silver, the equilibrium was not disturbed, although the
resistance of the one branch was a hundred times that of the
other. Very large fluid resistances certainly made it im-
possible to secure a disappearance of the sparks, and short air-
spaces introduced into one of the branches had a like effect.

The self-induction of iron wires for slowly alternating
currents is about eight to ten times as great as that of copper

36 ON VERY RAPID ELECTRIC OSCILLATIONS ii

wires of equal length and thickness. I therefore expected
that short iron wires would produce equilibrium with longer
copper wires. This expectation was not confirmed; the
branches remained in equilibrium when a copper wire was
replaced by an iron wire of equal length. If the theory of
the observations here given is correct, this can only mean that
the magnetism of iron is quite unable to follow oscillations so
rapid as those with which we are here concerned, and that it,
therefore, is without effect. A further experiment which will
be described below appears to point in the same direction.

Induction-Effects of unclosed Currents

The sparks which occur in the preceding experiments owe
their origin, according to our supposition, to self-induction,
but if we consider that the induction-effects, in question are
derived from exceedingly weak currents in short, straight con-
ductors, there appears to be good reason to doubt whether
these do really account satisfactorily for the sparks. In order
to settle this doubt I tried whether the observed electrical
disturbances did not manifest effects of corresponding magni-
tude in neighbouring conductors. I therefore bent some
copper wire into the form of rectangular circuits, about
10-20 cm. in the side, and containing only very short
spark-gaps. These were insulated and brought near to the
conductors in which the disturbances took place, and in such
a position that a side of the rectangle was parallel to the con-
ductor. When the rectangle was brought sufficiently near, a
stream of sparks in it always accompanied the discharges of
the induction-coiL These sparks were most brilliant in the
neighbourhood of the discharger, but they could also be
observed along the wire leading to the side-circuit as well
as in the branches of the latter. The absence of any direct
discharge between the inducing and induced circuits was care-
fully verified, and was also prevented by the introduction of a
solid insulator. Thus it is scarcely possible that our concep-
tion of the phenomenon is erroneous. That the induction
between two simple straight lengths of wire, traversed by only
small quantities of electricity, can yet become strong enough
to produce sparks, shows again the extraordinary shortness of

ON VERY RAPID ELECTRIC OSCILLATIONS

P C r- ) 3

the time in which these small quantities of electricity must
pass backwards and forwards along the conductors.

In order to study the phenomena more closely, the
rectangle which at first was employed as the side-circuit was
again brought into use, but this time as the induced circuit.
Along the short side of this (as indicated in Fig. 8) and at
a distance of 3 cm. from
it was stretched a second
copper wire g A, which was
placed in connection with
any part of the discharger.
As long as the end h of
the wire g h was free, only
weak sparks appeared in the
micrometer M, and these
were due to the discharge-
current of the wire g h, Blit
if an insulated conductor
(7— one taken from an elec-
trical machine — was then
attached to A, so that larger
quantities of electricity had
to pass through the wire,
sparks up to two milli-
metres long appeared in the micrometer. This was not caused
by an electrostatic effect of the conductor, for if it was attached
to g instead of to A, it was without effect ; and the action
was not due to the charging-current of the conductor, but to
the sudden discharge brought about by the sparks. For when
the knobs of the discharger were drawn so far apart that
sparks could no longer spring across it, then the sparks dis-
appeared completely from the induced circuit as welL Not
every kind of spark produced a sufl&ciently energetic discharge;
here, again, only such sparks as were before found to occasion
powerful side-sparks were found to be effective in exciting
the inductive action. The sparks excited in the secondary
circuit passed not only between the knobs of the micrometer
but also from these to other insulated conductors held near.
The length of the sparks was notably diminished by attaching
to the knobs conductors of somewhat large capacity or touch-

i 9

Fig. 8.

38 ON VERY RAPID ELECTRIC OSCILLATIONS ii

ing one of them with the hand ; clearly the quantities of
electricity set in motion were too small to charge conductors
of rather large capacity to the full potential On the other
hand, the sparking was not much affected by connecting the
two micrometer-knobs by a short wet thread. No physiological
effects of the induced current could be detected ; the secondary
circuit could be touched or completed through the body without
experiencing any shock.

Certain accessory phenomena induced me to suspect that
the reason why the electric disturbance in the wire g h pro-
duced such a powerful inductive action lay in the fact that it
did not consist of a simple chargmg-current, but was rather of
an oscillatory nature. I therefore endeavoured to etrengtheu
the induction by modifying the conditions so as to make them
more favourable for the production of powerful oscillations.
The following arrangement of the experiment suited my pur-
pose particularly well. I attached the conductor C as before
to the wire g h and then separated the micrometer-knobs so far
from each other that sparks only passed singly. I then
attached to the free pole of the discharger k (Fig. 8) a second
conductor C of about the same size as the first. The sparking
then again became very active, and on drawing the micrometer-
knobs still farther apart decidedly longer sparks than at first
could be obtained. This cannot be due to any direct action
of the portion of the circuit ik, for this would diminish the
effect of the portion gh\ it must, therefore, be due to the
action of the conductor C' upon the discharge-current of C.
Such an action would be incomprehensible if we assumed that
the discharge of the conductor C was aperiodic. It becomes,
however, intelligible if we assume that the inducing current in
g h consists of an electric oscillation which, in the one case,
takes place in the circuit C — wire gh — discharger, and in the
other in the system C — ^wire g h, wire i k — C It is clear in
the first place that the natural oscillations of the latter system
would be the more powerful, and in the second place that
the position of the spark in it is more suitable for exciting
the vibration.

Further confirmation of these views may be deferred for
the present. But here we may bring forward in support of them
the fact that they enable us to give a more correct explanation

II ON VERY RAPID ELECTRIC OSCILLATIONS 39

of the part which the discharge of the Buhmkorff coil plays in
the experiment. For if oscillatory disturbances in the circuit
C — Gf are necessary for the production of powerful induction-
effects, it is not sufficient that the spark in this circuit should
be established in an exceedingly short time, but it must also
reduce the resistance of the circuit below a certain value, and
in order that this may be the case the current-density from
the very start must not fall below a certain limit. Hence it is
that the inductive effect is exceedingly feeble when the con-
ductors C and Cf are charged by means of an electrical
machine ^ (instead of a Euhmkorff coil) and then allowed to
discharge themselves ; and that it is also very feeble when a
small coil is used, or when too large a spark-gap is introduced ;
in all these cases the motion is aperiodic. On the other hand, a
powerful discharge from a Euhmkorff coil gives rise to oscilla-
tions, and therefore to powerful disturbances all round, by per-
forming the following functions : — In the first place, it charges
the ends C and Cf of the system to a high potential; secondly,
it gives rise to a disruptive discharge ; and thirdly, after starting
the discharge, it keeps the resistance of the air-gap so low that
oscillations can take placa It is known that if the capacity
of the ends of the system is large — ^if, for example, they consist
of the armatures of a battery of Leyden jars — the discharge-
current from these capacities is able of itself to reduce the
resistance of the spark-gap considerably ; but when the capaci-
ties are small this function must be performed by some ex-
traneous discharge, and for this reason the discharge of the
induction-coil is, under the conditions of our experiment,
absolutely necessary for exciting oscillations.

As the induced sparks in the last experiment were several
millimetres long, I had no doubt that it would be possible to
obtain sparks even when the wires used were much farther
apart ; I therefore tried to arrange a modification of the ex-
periment which appeared interesting. I gave the inducing
circuit the form of a straight line (Fig. 9). Its ends were
formed by the conductors C and Cf. These were 3 metres
apart, and were connected by a copper wire 2 mm. thick, at
the centre of which was the discharger of the induction-coil.
The induced circuit was the same as in the preceding experi-

^ [See Note 3 at end of book.]

ON YEBT RAPID ELECTBIG OSCILLATIONS

ment, 120 cm. long and 80 cm. broad. If the shortest
distance between the two systems was now made equal to
50 cm., induced sparks 2 mm. in length could still be
obtained ; at greater distances the spark -length decreased

<zi_>

-o»-

Fig. 9.

rapidly, but even when the shortest distance was 1;5 metres, a
continuous stream of sparks was perceptible. The experiment
was in no way interfered with if the observer moved between
the inducing and induced systems. A few control-experiments
again established the fact that the phenomena observed were
really caused by the current in the rectilinear portion. If one
or both halves of this were removed, the sparks in the micro-
meter ceased, even when the coil was still in action. They also
ceased when the knobs of the discharger were drawn so far apart
as to prevent any sparking in it. Inasmuch as the difference
of electrostatic potential at the ends of the conductors C and C
are now greater than before, this shows that these differences
of potential are not the cause of the sparks in the micrometer.
Hitherto the induced circuit was closed ; it was, however,
to be supposed that the induction would take place equally in
an open circuit. A second insulated copper wire was therefore
stretched parallel to the straight wire in the preceding arrange-
ment, and at a distance of 60 cm. from it. This second wire
was shorter than the first; two insulated spheres 10 cm. in
diameter were attached to its ends and the spark-micrometer
was introduced in the middle of it. When the coil was now

II ON VEBY RAPID ELECTRIC OSCILLATIONS 41

started, the stream of sparks from it was accompanied by a
similar stream in the secondary conductor. But this experi-
ment should be interpreted with caution, for the sparks observed
are not solely due to electromagnetic induction. The alter-
nating motion in the system C (/ is indeed superposed upon
the Buhmkorff discharge itself. But during its whole course
the latter determines an electrification of the conductor C, and
an opposite electrification of the conductor Cf. These electri-
fications had no effect upon the closed circuit in the preceding
experiment, but in the present discontinuous conductor they
induce by purely electrostatic action opposite electrifica-
tion in the two parts of the conductor, and thus produce
sparks in the micrometer. In fact, if we draw the knobs of
the discharger so far apart that the sparks in it disappear, the
sparks in the micrometer, although weakened, still remain.
These sparks represent the effect of electrostatic induction,
and conceal the effect which alone we desired to exhibit. -

There is, however, an easy way of getting rid of these
disturbing sparks. They die away when we interpose a bad
conductor between the knobs of the micrometer, which is most
simply done by means of a wet thread.) The conductivity of
this is obviously good enough to allow the current to follow
the relatively slow alternations of the discharge from the coil ;
but in the case of the exceedingly rapid oscillations of the
rectilinear circuit it is, as we have already seen, not good
enough to bring about an equalisation of the electrifications.
If after placing the thread in position we again start the
sparking in the primary circuit, vigorous sparking begins again
in the secondary circuit, and is now solely due to the rapid
oscillations in the primary circuit I have tested to what
distance this action extended. Up to a distance of 1*2 metres
between the parallel wires the sparks were easily perceptible ;
the greatest perpendicular distance at which regular sparking
could be observed was 3 metres. Since the electrostatic effect
diminishes more rapidly with increasing distance than the
electromagnetic induction, it was not necessary to complicate
the experiment by using the wet thread at greater distances,
for, even without this, only those discharges which excited
oscillations in the primary wire were attended by sparks in the
secondary circuit.

42 ON VERY RAPID ELECTRIC OSCILLATIONS ii

I believe that the mutual action of rectilinear open circuits
which plays such an important part in theory is, as a matter
of fact, illustrated here for the first time. ^

Besonance Phenomena

We may now regard it as having been experimentally
proved that currents of rapidly varjdng intensity, capable of
producing powerful induction-effects, are present in conductors
which are connected with the discharge circuit. The existence
of regular oscillations, however, was only assumed for the pur-
pose of explaining a comparatively small number of phenomena,
which might perhaps be accounted for otherwise. But it
seemed to me that the existence of such oscillations might be
proved by showing, if possible, symphonic relations between
the mutually reacting circuits. According to the principle of
resonance, a regularly alternating current must (other things
being similar) act with much stronger inductive effect upon a
circuit having the same period of oscillation than upon one of
only slightly different period.^ If, therefore, we allow two
circuits, which may be assumed to have approximately the
same period of vibration, to react on one another, and if we
vary continuously the capacity or coeflBcient of self-induction
of one of them, the resonance should show that for certain
values of these quantities the induction is perceptibly stronger
than for neighbouring values on either side.

The following experiments were devised in accordance with
this principle, and, after a few trials, they quite answered my
intention. The experimental arrangement was very nearly the
same as that of Fig. 9, excepting that the circuits were made
somewhat different in size. The primary conductor was a
perfectly straight copper wire 2*6 metres long and 5 mm.
thick. This was divided in the middle so as to include the
spark-gap. The two small knobs between which the discharge
took place were mounted directly on the wire and connected
with the poles of the induction-coil. To the ends of the wire
were attached two spheres, 30 cm. in diameter, made of strong
zinc-plate. These could be shifted along the wire. As they
formed (electrically) the ends of the conductor, the circuit

1 Of. Oberbeck, JVicd. Ann. 26, p. 245, 1885,

II ON VEBY RAPID ELECTRIC OSCILLATIONS 43

could easily be shortened or lengthened. The secondary
circuit was proportioned so that it was expected to have a
somewhat smaller period of oscillation than the primary; it
was in the form of a square 75 cm. in the side, and was made
of copper wire 2 mm. in diameter. The shortest distance
between the two systems was made equal to 30 cm., and at
first the primary current was allowed to remain of full length.
Under these circumstances the length of the biggest spark in
the induced circuit was 0*9 mm. When two insulated metal
spheres of 8 cm. diameter were placed in contact with the
two poles of the circuit, the spark-length increased, and could
be made as large as 2*5 mm. by suitably diminishing the dis-
tance between the two spheres. On the other hand, if two
conductors of very large surface were placed in contact with
the two poles, the spark-length was reduced to a small fraction
of a millimetre. Exactly similar results followed when the
poles of the secondary circuit were connected with the plates
of a Kohlrausch condenser. When the plates were far apart
the spark-length was increased by increasing the capacity, but
when they were brought closer together the spark-length again
fell to a very small value. The easiest way of adjusting the
capacity of the secondary circuit was by hanging over its two
ends two parallel bits of wire and altering the length of these
and their distance apart. By careful adjustment the sparking
distance was increased to 3 mm., after which it diminished,
not only when the wires were lengthened, but also when they
were shortened. That an increase of the capacity should
diminish the spark-length appeared only natural ; but that it
should have the effect of increasing it can scarcely be explained
excepting by the principle of resonance.

If our interpretation of the above experiment is correct,
the secondary circuit, before its capacity was increased, had a
somewhat shorter period than the primary. Eesonance should
therefore have occurred when the rapidity of the primary
oscillations was increased. And, in fact, when I reduced the
length of the primary circuit in the manner above indicated,
tlie sparking distance increased, again reached a maximum of
3 mm. when the centres of the terminal spheres were 1*5
metres apart, and again diminished when the spheres were
brought still closer together. It might be supposed that the

44 ON VERY RAPID ELECTRIC OSCILLATIONS ii

spark-length would now increase still further if the capacity of
the secondary circuit were again, as before, increased. But
this is not the case ; on attaching the same wires, which before
had the eflfect of increasing the spark-length, this latter falls
to about 1 mm. This is in accordance with our conception of
the phenomenon ; that which at first brought about an equality
between the periods of oscillation now upsets an equality which
has been attained in another way. The experiment was most
convincing when carried out as follows : — ^The spark-micrometer
was adjusted for a fixed sparking distance of 2 mm. If the
secondary circuit was in its original condition, and the primary
circuit 1*5 metres long, sparks passed regularly. If a small
capacity is added to the secondary circuit in the way already
described, the sparks are completely extinguished; if the
primary circuit is now lengthened to 2*6 metres they reappear;
they are extinguished a second time if the capacity added to
the secondary circuit is doubled ; and by continuously increas-
ing the capacity of the already lengthened primary circuit
they can be made to appear and disappear again and again.
The experiment shows us quite plainly that effective action is
determined, not by the condition of either of the circuits, but
by a proper relation (or harmony) between the two.

The length of the induced sparks increased considerably
beyond the values given above when the two circuits were
brought closer together. When the two circuits were at a
distance of 7 cm. from one another and were adjusted to exact
resonance, it was possible to obtain induced sparks 7 mm.
long; in this case the electromotive forces induced in the
secondary circuit were almost as great as those in the primary.

In the above experiments resonance was secured by alter-
ing the coefficient of self-induction and the capacity of the
primary circuit, as well as the capacity of the secondary
circuit. The following experiments show that an alteration
of the coefficient of self-induction of the secondary circuit can
also be used for this purpose. A series of rectangles abed
(Fig. 9) were prepared in which the sides a b and c d were kept
of the same length, but the sides a c and b d were made of wires
varying in length from 10 cm. to 250 cm. A marked maxi-
mum of the sparking distance was apparent when the length
of the rectangle was 1'8 metres. In order to get an idea of

ON VERY RAPID ELECTRIC OSCILLATIONS

the quantitative relations I measured the longest sparks which
appeared with various lengths of the secondary circuit Fig.
10a shows the results.^ Abscissae represent the total length
of the induced circuit and ordinates the maximum spark-
length. The points indicate the observed values. Measure-
ments of sparking distances are always very uncertain, but this
uncertainty cannot be such as to vitiate the general nature of
the result. In another
set of experiments not
only the lengths of the
sides a h and c d, but
also their distance apart
(30 cm.), and their posi-
tion were kept constant ;
but the sides a c and h d
were formed of wires
of gradually increasing
length coiled into loose
spirals. Fig. 106 shows
the results obtained.
The maximum here cor-
responds with a some-
what greater length of
wire than before. Prob-
ably this is because the
lengthening of the wire
in this case increases
only the coefficient of
self- induction, whereas

in the former case it ^o ^oo tooa^

increased the capacity Fig. lo, a and 6.

as well.

Some further experiments were made in order to determine
whether any different result would be obtained by altering the
resistance of the secondary circuit. With this intention the
wire cd ol the rectangle was replaced by various thin copper
and German silver wires, so that the resistance of the secondary
circuit was made about a hundred times as large. This change
had very little effect on the sparking distance, and none at

^ [See Note 4 at end of book.]

•

2
4

-C

•

■

Jirahtlcinff

\o Jooo

• •

2
i

w% ^"

•

46 ON VERY RAPID ELECTRIC OSCILLATIONS ii

all on the resonance ; or, in other words, on the period of
oscillation.

The effect of the presence of iron was also examined. The
wire c d was in some experiments surrounded by an iron tube,
in others replaced by an iron wire. Neither of these changes
produced a perceptible effect in any sense. This again confirms
the supposition that the magnetism of iron cannot follow such
exceedingly rapid oscillations, and that its behaviour towards
them is neutral. Unfortunately we possess no experimental
knowledge as to how the oscillatory discharge of Leyden jars
is affected by the presence of iron.

Nodes

The oscillations which we excited in the secondary circuit,
and which were measured by the sparks in the micrometer,
are not the only ones, but are the simplest possible in that
circuit. While the potential at the ends oscillates backwards
and forwards continually between two limits, it always retains
the same mean value in the middle of the circuit. This
middle point is therefore a node of the electric oscillation,
and the oscillation has only this one node. Its existence
can also be shown experimentally, and that in two ways. In
the first place, it can be done by bringing a small insulated
sphere near the wire. The mean value of the potential of
the small sphere cannot differ appreciably from that of the
neighbouring bit of wire. Sparking between the knob and
the wire can therefore only arise through the potential of
the neighbouring point of the system experiencing sufficiently
large oscillations about the mean value. Hence there should
be vigorous sparking at the ends of the system and none
at all near the node. And this in fact is so, excepting,
indeed, that when the nodal point is touched the sparks do
not entirely disappear, but are only reduced to a minimum.
A second way of .showing the nodal point is clearer. Adjust
the secondary circuit for resonance and draw the knobs of
the micrometer so far apart that sparks can only pass by
the assistance of the action of resonance. If any point of
the system is now touched with a conductor of some capacity,
we should in general expect that the resonance would be

ON VERY RAPID ELECTRIC OSCILLATIONS

(d-

disturbed, and that the sparks would disappear ; only at the
node would there be no interference with the period of oscil-
lation. Experiment confirms this. The middle of the wire
can be touched with an insulated sphere, or with the hand,
or can even be placed in metallic connection with the gas-
pipes without aflfecting the sparks ; similar interference at the
side-branches or the poles causes the sparks to disappear.

After the possibility of fixing a nodal point was thus
proved, it appeared to me to be worth while experimenting
on the production of a vibration with two nodes. I pro-
ceeded as follows : — The straight primary conductor C Cf and
the rectilinear second-
ary abed were set up
as in the earlierexperi-
ments and brought to
resonance. An exactly

similar rectangle e/^A -T^^)

was then placed oppo- ^-^
site to abed as
shown in Fig. 11,
and the neighbouring
poles of both were
joined (1 with 3 and 2
with 4). The whole
system forms a closed
metallic circuit, and
the lowest or funda-
mental vibration pos-
sible in it has two nodes. Since the period of this vibra-
tion must very nearly agree with the period of either half, and
therefore with the period of the primary conductor, it was
supposed that vibrations ^yould develop having two anti-
nodes at the junctions 1-3 and 2-4, and two nodes at the
middle points ot ed and gh. l^hese vibrations were always
measured by the sparking distance between the knobs of the
micrometer which formed the poles 1 and 2. The results
of the experiment were as follows: — Contrary to what was
expected, it was found that the sparking distance between 1
and 2 was considerably diminished by the addition of the
rectangle efg h. From about 3 mm. it fell to 1 mm. Never-

Fig. n.

48 ON VERY RAPID ELECTRIC OSCILLATIONS ii

theless there was still resonance between the primary circuit
and the secondary. For every alteration of efg h reduced the
sparking distance still further, and this whether the alteration
was in the direction of lengthening or shortening the rectangle.
Further, it was found that the two nodes which were expected
were actually present. By holding a sphere near c d and g h
only very weak sparks could be obtained as compared with
those from a e and &/. And it could also be shown that these
nodes belonged to the same vibration which, when strengthened
by resonance, produced the sparks 1-2. For the sparking
distance between 1 and 2 was not diminished by touching along
cd OT gh, but it was by touching at every other place.

The experiment may be modified by breaking one of the
connections 1-3 or 2-4, say the latter. As the current-
strength of the induced oscillation is always zero at these
points, this cannot interfere much with the oscillation. And,
in fact, after the connection has been broken, it can be shown
as before that resonance takes place, and that the vibrations
corresponding to this resonance have two nodes at the same
places. Of course there was this difference, that the vibration
with two nodes was no longer the deepest possible vibration ;
the vibration of longest period would be one with a single
node between a and e, and having the highest potentials at
the poles 2 and 4. And if we bring the knobs at these
poles nearer together we find that there is feeble sparking
between them. We may attribute these sparks to an excita-
tion, even if only feeble, of the fundamental vibration; and
this supposition is made almost a certainty by the following ex-
tension of the experiment : — We stop the sparks between 1 and
2 and direct our attention to the length of the sparks between
2 and 4, which measures the intensity of the fundamental vibra-
tion. We now increase the period of oscillation of the primary
circuit by extending it to the full length and adding to its
capacity. We observe that the sparks thus increase to a
maximum length of several millimetres and then again become
shorter. Clearly they are longest when the oscillation of the
primary current agrees with the fundamental oscillation. And
while the sparks between 2 and 4 are longest it can be easily
shown that at this time only a single nodal point corresponds
to these sparks. For only between a and e can the conductor

II ON VERY RAPID ELECTRIC OSCILLATIONS 49

be touched without interfering with the spaxks, whereas touch-
ing the previous nodal points interrupts the stream of sparks.
Hence it is in this way possible, in any given conductor, to
make either the fundamental vibration or the first overtone
preponderate.

Meanwhile, there are several further problems which I
have not solved; amongst others, whether it is possible to
establish the existence of oscillations with several nodes. The
results already described were only obtained by careful atten-
tion to insignificant details ; and so it appeared probable that
the answers to further questions would turn out to be more or
less ambiguous. The difficulties which present themselves
arise partly from the nature of the methods of observation,
and partly from the nature of the electric disturbances observed.
Although these latter manifest themselves as undoubted oscil-
lations, they do not exhibit the characteristics of perfectly
regular oscillations. Their intensity varies considerably from
one discharge to another, and from the comparative unimport->
ance of the resonance-effects we conclude that the damping
must be rapid; many secondary phenomena point to the
superposition of irregular disturbances upon the regular oscilla-
tions, as, indeed, was to be expected from the complex nature
of the system of conductors. If we wish to compare, in
respect of their mathematical relations, our oscillations with
any particular kind of acoustic oscillations, we must not choose
the long-continued harmonic oscillations of uniform strength
which are characteristic of tuning-forks and strings, but rather
such as are produced by striking a wooden rod with a hammer,
— oscillations which rapidly die away, and with which are
mingled irregular disturbances.^ And when we are dealing
with oscillations of the latter class we are obliged, even in
acoustics, to content ourselves with mere indications of re-
sonance, formation of nodes, and similar phenomena.

For the sake of those who may wish to repeat the experi-
ments and obtain the same results I must add one remark, the
exact significance of which may not be clear at first In all
the experiments described the apparatus was set up in such a
way that the spark of the induction-coil was visible from the
place where the spark in the micrometer took place. When

^ [See Note 5 at end of book.]

^ OF THE ^

UNIYEKSITT

50 ON VERY KAPID ELECTRIC OSCILLATIONS ii

this is not the case the phenomena are qualitatively the same,
but the spark-lengths appear to be diminished. I have under-
taken a special investigation of this phenomenon, and intend to
publish the results in a separate paper.^

Theoreticdl

It is highly desirable that quantitative data respecting the
oscillations should be obtained by experiment. But as there
is at present no obvious way of doing this, we are obliged to
have recourse to theory, in order to obtain at any rate some
indication of the data. The theory of electric oscillations
which has been developed by Sir W. Thomson, v. Helmholtz,
and Kirchhoff has been verified as far as the oscillations of
open induction-coils and oscillatory Leyden jar discharges
are concerned ; ^ we may therefore feel certain that the appli-
cation of this theory to the present phenomena will give
results which are correct, at least as far as the order of
magnitude is concerned.

To begin with, the period of oscillation is the most im-
portant element. As an example to which calculation can
be applied, let us determine the (simple or half) period of
oscillation T of the primary conductor which we used in the
resonance-experiments. Let P denote the coeflBcient of self-
induction of this conductor in magnetic measure, expressed
in centimetres ; C the capacity of either of its ends in electro-
static measure (and therefore expressed also in centimetres) ;
and finally A the velocity of light in centimetre/seconds.

Then, assuming that the resistance is small, T = 7rvPC/A.
In our experiments the capacity of the ends of the conductor
consisted mainly of the spheres attached to them. We shall
therefore not be far wrong if we take C as being the radius of
either of these spheres, or put C = 1 5 cm.^ As regards the
coefficient of self-induction P, it was that of a straight wire, of
diameter c^= 0*5 cm., and of which the length L was 150 cm.
when resonance occurred. Calculated by Neumann's formula
P =Jfcos e/r ds ds', the value of P for such a wire is

^ [See IV., p. 63.] ^ Lorenz, Wied, Ann. 7, p. 161, 1879. '

^ [See Note 6 at end of book.]

II ON VERY RAPID ELECTRIC OSCILLATIONS 51

2L{lognat(4L/d) — 0*75} and therefore in our experiments
P=1902 cm.

At the same time we know that it is not certain whether
Neumann's formula is applicable to open circuits. The most
general formula, as given by v. Helmholtz, contains an un-
determined constant k, and this formula is in accordance with
the known experimental data. Calculated according to the
general formula, we get for a straight cylindrical wire of
length L and diameter d the value P = 2L{log nat (4L/rf) —
0'75 +^(1 — lc)Y If in this we put k = 1, we arrive at Neu-
mann's value. If we put A = 0, or A; = — 1, we obtain values
which correspond to Maxwell's theory or Weber's theory. If we
assume that one at any rate of these values is the correct one,
and therefore exclude the assumption that it may have a very
large negative or positive value, then the true value of k is not
of much moment. For the coefficients calculated with these
various values of k differ from each other by less than one-
sixth of their value; and so if the coefficient 1902 does not
exactly correspond to a length of wire of 150 cm., it does
correspond to a length of our primary conductor not differing
greatly therefrom. From the values of P and C it follows

that the length ttvCP is 531 cm. This is the distance
through which light travels in the time of an oscillation, and
is at the same time the wave-length of the electromagnetic
waves which, according to Maxwell's view, are supposed to be
the external effect of the oscillations. From this length it
foUows that the period of oscillation itself (T) is 1*77 hundred-
millionths of a second ; thus the statement which we made in
the beginning as to the order of magnitude of the period is
justified.

Let us now turn our attention to what the theory can tell
us as to the ratio of damping of the oscillations. In order
that oscillations may be possible in the open circuit, its resist-
ance must be less than 2AvP/C For our primary con-
ductor >s/P/C = 11*25 : now since the velocity A is equal to
30 earth-quadrant/seconds, or to 30 ohms, it follows that the
limit for r admissible in our experiment is 676 ohms. It is
very probable that the true resistance of a powerful discharge
lies below this limit, and thus from the theoretical point of
view there is no contradiction of our assumption of oscillatory

5^ ON VERY RAPID ELECTRIC OSCILLATIONS ' ii

motion. If the actual value of the resistance lies somewhat
below this limit, the amplitude of any one oscillation would
bear to the amplitude of that immediately following the ratio
of 1 to «-<'^/2P). rjij^g number of oscillations required to reduce
the amplitude in the ratio of 2*71 to 1 is therefore equal to

2P/rT or 2 A s/VjCjirr. It therefore bears to 1 the same
ratio that I/tt of the calculated limiting value bears to the
actual value of the resistance, or the same ratio as 215 ohms
to r. Unfortunately we have no means of even approximately
estimating the resistance of a spark-gap. Perhaps we may
regard it as certain that this resistance amounts to at least a
few ohms, for even the resistance of strong electric arcs does
not fall below this. It would follow from this that the
number of oscillations we have to consider should be counted
by tens and not by hundreds or thousands.^ This is in complete
accordance with the character of the phenomena, as has already
been pointed out at the end of the preceding section. It is
also in accordance with the behaviour of the very similar
oscillatory discharges of Leyden jars, in which case the
oscillations of perceptible strength are similarly limited to a
very small number.

In the case of purely metallic secondary circuits the condi-
tions are quite different from those of the primary currents to
which we have confined our attention. In the former a
disturbance would, according to theory, only come to rest
after thousands of oscillations. There is no good reason for
doubting the correctness of this result ; but a more complete
theory would certainly have to take into consideration the
reaction upon the primary conductor, and would thus probably
arrive at higher values for the damping of the secondary con-
ductor as well.

Finally, we may raise the question whether the induction-
effects of the oscillations which we have observed were of the
same order as those which theory would lead us to expect, or
whether there is here any appearance of contradiction between
the phenomena themselves and our interpretation of them.
We may answer the question by the following considerations : —
We observe, in the first place, that the maximum value of the
electromotive force which the oscillation induces iq its own

^ [See Note 7 at end of book.]

II ON VERY RAPID ELECTRIC OSCILLATIONS 53

circuit must be very nearly equal to the maximum diflference
of potential at the ends, for if the oscillations were not damped,
there would exist complete equality between the two magni-
tudes ; inasmuch as the potential difference of the ends and
the electromotive force of induction would in that case be in
equilibrium at every instant Now in our experiments the
potential difference between the ends was of a magnitude
corresponding to a sparking distance of 7-8 mm., and any such
sparking distance fixes the value of the greatest inductive
effect of the oscillation in its own path. We observe, in
the second place, that at every instant the induced electro-
motive force in the secondary circuit bears to that induced
in the primary circuit the same ratio as the coefficient of
mutual induction p between the primary and secondary
circuits bears to the coefficient of self-induction P of the
primary circuit. There is no difficulty in calculating accord-
ing to known formulae the approximate value of p for our
resonance-experiments. It was found to vary in the different
experiments between one-ninth and one-twelfth of P. From
this we may conclude that the maximum electromotive force
which our oscillation excites in the secondary circuit should be
of such strength as to give rise to sparks of ^/g to Yg mm.
in length. And accordingly the theory allows us, on the one
hand, to expect visible sparks in the secondary circuit under
all circumstances, and, on the other hand, we see that we can
only explain sparks of several millimetres in length by assum-
ing that several successive inductive effects strengthen each
other. Thus from the theoretical side as well we are com-
pelled to regard the phenomena which we have observed as
being the results of resonance.

Further application of theory to these phenomena can only
be of service when we shall have succeeded by some means in
determining the period of oscillation directly. Such measure-
ment would not only confirm the theory but would lead to an
extension of it. The purpose of the present research is simply
to show that even in short metallic conductors oscillations can
be induced, and to indicate in what manner the oscillations
which are natural to them can be excited.

Ill

FROM HERE W. VON BEZOLD'S PAPER : " RESEARCHES
ON THE ELECTRIC DISCHARGE — PRELIMINARY
COMMUNICATION "

{Poggendorff*8 Anncdeny 140, p. 541. Berichte der Bayrischen. Akad, d.

fFissensch,, 1870.)

As we must extract that part of v. Bezold's work which
alone concerns us here, and remove it from its context, it may
be advisable to preface it by some explanation.

Von Bezold's researches start with observations on lichten-
berg dust-figures. Herr von Bezold had noticed that under
certain conditions the characters of the positive and negative
figures appeared to undergo some modification and to resemble
each other more nearly ; so much so that the negative figure,
for example, might be taken for positive. The first deviation
from the normal character always presents itself in the form of
a small positive figure appearing in the centre of the negative
figure, or a small negative figure in the centre of the positive
figura It appeared that the more complicated figures always
owed their origin to a spark associated with an alternating
discharge, while the simple figures were produced by simple
discharges. In every complicated figure an alternating dis-
charge to a certain extent registered itself ; and from the
appearance of the figure the alternating character of the
discharge and the direction of its first outburst could be
directly recognised. We can, therefore, make use of the
Lichtenberg figures in investigating the discharge.

Von Bezold produced the Lichtenberg figures in the
following way : — A horizontal plate of well-insulating glass was

Ill V. bezold's researches on the electric discharge 55

covered underneath with tinfoil, and this was connected to
earth. On the upper side of the plate was placed the point
of a vertical knitting-needle, to which the discharge was led.
The needle was then removed, the plate dusted, and the
figure produced was examined. K this arrangement (which
will be called the test -plate) is inserted directly in the
discharge -circuit of a Leyden jar or of the conductor of
an electrical machine, it naturally makes it impossible for
an alternating discharge, and in general for any complete
discharge, to occur. Hence the test -plate can only be
inserted in a shunt to the actual discharge which is being
investigated.

While Herr von Bezold was carrying out this method —
using the discharge to earth of the conductor of his electrical
machine as the principal discharge — he at once came upon
certain very remarkable phenomena. Positive figures made
their appearance where negative ones were to be expected;
large figures appeared where one might have supposed there
would be small ones, and vice versa. Ohm's law did not explain
the facts ; it appeared as if the electricity in motion had the
power of carrying with it neighbouring electrifications, as if
" phenomena occurred in electrical disturbances similar to those
which are observed in the motion of fluids under the name of
aspiration-phenomena." Of course many of the details were
bound to remain unexplained at first. We now quote Herr
von Bezold's own words :

" These peculiar observations led to further researches on
the division of electrical discharge-currents.

" Here, again, alternating discharges gave more constant
results than simple ones ; care was therefore taken to provide
always a suitable return-conductor. The above experiments
show that a simple wire cannot be employed for this purpose ;
hence the induction-coil of the Euhmkorflf R was used . as a
return-conductor.

" If now the electrical machine Q was slowly turned until a
spark passed at F, complex positive figures appeared with great
regularity on the plate at A.

" If a portion of the current was diverted along a short wire
D, and this branch-current led on to the plate in the same way

56 V. BEZOLD'S researches on the electric discharge III

by a conductor B, there appeared, as might be expected, two
precisely similar figures. If, on the other hand, the branch- wire

was of considerable
length (somewhat
more than 1 metre),
there was a decided
difference in size be-
tween the figures.
As soon as the
length of the wire
exceeded this limit,
the figure at B was
always larger than
at A, even when the
branch had its origin quite near the end of the conductor
(1 cm. above the plate). The difference in size between the
two figures became more striking as the length of the branch-
wire D was increased, until finally, when D was equal to 6*4
metres, and F (the length of the spark-gap) was equal to
4*0 mm., the figure at A was reduced to a small star, and
often was altogether absent

" This experiment obviously shows that Ohm's law only holds
good for stationary currents, Ld not for electrical discharges,
as indeed all theoretical investigations have shown. For
whereas no electricity reaches the plate through the short
branch A^ it rushes, at any rate apparently, along the path
through the wire D which is several hundred times longer.

" If the wire D is still further lengthened there is (within
fairly wide limits) no change at first to be observed; only
when the length has been about doubled does the figure at A
again become larger, until with still greater lengths the
difference in size between the two figures again completely
disappears. It made no difference whether the wire used was
thick or thin, whether it was a good or bad conductor, nor yet
whether it was tightly stretched or curved. I have not yet
experimented with wire spirals.

" On account of the complete novelty of the phenomena it
appeared to me of interest to investigate the behaviour of the

Ill

V. bezold's researches on the electric discharge 57

Fig. 13.

wire D at different places. For this purpose a modification
shown in Fig. 13 was made. On the plate were placed the
conductors Ay B, C, which were connected together by two
wires D and H. If the length of these wires is chosen so as
to produce as large as pos-
sible a figure at C, and, on jo b'
the other hand, as small as
possible a figure at Ay then
the figure at .S is larger than
that at A and smaller than
that at G, If the wires are
longer the sizes of the
figures A and C are more
nearly equal, whereas, when
the ratio D:B' is suit-
ably chosen, B becomes
quite small and even dis-
appears altogether. When

the sparking distance was 4'3 mm. and the length A P
was equal to 50 cm., D=&'2 m. and D — 8*1 m., the figures
at A and C were large, whereas only a small star appeared
at ^.

" If any one of the conductors is lifted away from the plate,
the figures at the remaining conductors are not in the least
altered thereby.

" This experiment teaches us a new fact, viz. that by simply
connecting a conductor with a wire which has a blind end, we
can produce important modifications in the figure which is
formed by that conductor, and may even cause it to disappear.
The most instructive way of performing the experiment is to
bring near the conductor A a second spark-micrometer / (Fig.
14), one knob of which is connected with A while the other
leads to the wire D. If now the distance between the knobs
of the micrometer / is at first made large and then gradually
diminished, it is seen that at the instant when the spark passes
at / the figure at A becomes altered or disappears. But if we
consider that in the case of an alternating discharge the wire
forthwith becomes completely discharged, it follows that in
such a case electricity is first driven to the outer end of the

58 V. BEZOLD'S researches on the electric discharge III

wire Dy and then immediately back again ; that, in fact, we have
here disturbances which are entirely comparable with reflection.

Fig. 14.

" This consideration leads to an hypothesis respecting the
peculiar changes of size which the dust-figures undergo when
the discharge ^branches as above described.

" If electric waves are impelled along a wire and forced to
return along the same path after reflection at the end, the
advancing and reflected waves would interfere and so give rise
to phenomena analogous to those observed in organ -pipes.
The observations already described point distinctly to such an
analogy, and we may venture to compare the positions of the
wire in which maximum and minimum figures appear with the
antinodes and nodes.

" The hypothesis that the phenomena under discussion are
due to interference gains additional support from the fact that
it is only with alternating currents that the experiment is a
decided success; differences in size between the various figures
are indeed observed with simple discharges too, but not nearly
to the same extent.

" In connection with the above experiments, a small modifi-
cation was tried, which in turn became the starting-point for
fresh researches : —

" If the end of the wire D (Fig 12) is brought back to and
connected with the first conductor A, as shown in the accom-
panying diagram, the figure can again be made to disappear by
suitably choosing the length of the wire. Strictly speaking,
this experiment was the starting-point of all the others already
described ; but I have deferred the description of it until now

Ill V. bezold's reseakches on the electric discharge 69

because it does not help us much to understand the above ex-
periments. For my own part, I at first believed that I had

Fig. 15.

found in it an analogue to Savart's interference-experiment for
sound-waves, and pictured the currents to myself as moving in
the direction of the dotted arrows. This view was upset by
the experiments in which the wire with a blind end was used,
as well as by the fact that the distance between the two points
of divergence on A exercised no decided effect on the result.
In order to remove all doubt on this score I introduced a spark-
gap into the branch D at various places in turn. The knobs
of this second micrometer were only 0*01 to 0*03 mm. apart.
I reasoned thus : If the current enters the wire from both ends
there must be some point on the wire at which the two trains
of waves meet When the spark-gap is exactly at this point,
the potential on the two balls must reach the same value
simultaneously, and there can be no cause for the production
of sparks at this point ; whereas, at all other points, sparking
was to be expected.

" And, as a matter of fact, the sparking ceased when the
micrometer was introduced in the middle of a branch, and
began again as soon as it was removed from this point a few
decimetres on either side. It is thus proved that the direction
of the current is as indicated by the continuous arrows ; and,
on the other hand, the small retardation which the electric
discharge-current suffers while traversing a few decimetres of
wire is here made evident.

" I now endeavoured chiefly to find out under what experi-
mental conditions this retardation was most effectively shown. I
found it best to use the direct discharge of a Euhmkorfif coil,

60 V. BEZOLD's researches on the electric discharge III

as shown in the diagram (Fig. 16). The inducing current was
provided by a Grove cell, and the sparking distance F in the

Fig. 16.

spark-micrometer was made about 2 mm., inasmuch as neither
larger nor smaller spark-gaps gave such good results.

" Under these circumstances it sufl&ced for the production of
the spark if one of the wires D was only one decimetre longer
than the other. On the contrary, no spark ever appeared if they
were of the same length. It can, however, be made to appear
at once if the symmetry of the two branches is upset by placing
the knob of a Leyden jar in contact with one of the wires.

" In this experiment, again, the material and thickness of
the wires had not the slightest effect. Whether I used a
silvered copper wire of 0*06 mm. diameter, or an iron wire of
0*23 mm., or a copper wire of 0*80 mm. diameter, there was
never any spark as long as the two wires were of equal length.

" Thus the velocity of electricity for all (stretched) ^ wires
is the same.

" The experiment is still not easily visible in the form above
described, for one can only work with a smaH spark-gap in the
auxiliary micrometer/. I therefore endeavoured to modify it
in such a way as would admit of its being exhibited in a lecture-
room.

" Trials with small Geissler tubes gave no definite result.
On the other hand, the retardation can be very well shown in
the following way, provided the difference of path amounts to
a few meters (Fig. 17) : —

" Let a (negative) discharge, preferably from a Euhmkorflf
coil, be divided as above directly beyond the spark-micrometer
into two branches. Let one of them be connected with the
coating of a completely insulated test-plate, while the other is

^ Wires wound spirally would probably have given a different result.

Ill V. bezold's researches on the electric discharge 61

led by the conductor -4 on to the upper uncovered surface.
Under these conditions a positive figure, or a negative one, or
no figure at all, may appear on the upper surface according as
the upper branch is larger, smaller, or of the same length as
the lower. Indeed, we can predict what results the experiments
must give if the supposition is correct that they are caused by
time-differences. For if we recollect that the effect of leading

Fig. 17.

positive electricity on to the plate is the same as the effect of
removing negative electricity, we can understand how a positive
discharge gives rise to a positive figure if the electricity reaches
the point of the conductor before it reaches the coating, i.e. if
D^ is shorter than D^ If, on the other hand, the discharge
arrives first at the coating, the induced electricity traverses
the conductor in the opposite sense, and hence a negative
figure must make its appearance upon the pane as soon as
2>2 is shorter than D^. In the course of the disturbance the
induced charge in the wire D^ must meet the electricity
arriving directly from F, and hence a complex character will
be impressed upon the figure.

"Between these two dispositions, which give opposite
results, there obviously must be another in which no figure
can be produced, because there is no reason why the one kind
or the other should appear. This must be the case when the
electricity arrives simultaneously from both sides, i.e. when
Di and i^g ^^e of the same length.^

" The experiments entirely coincided with these theoretical
predictions. With either kind of electricity figures of both
kinds can be obtained if the lengths of the wires are rightly
chosen.

^ A small difference of length in favour of the upper wire may occur here,
inasmuch as the electricity arriving from below has to spread itself out over the
whole coating.

62 V. BEZOLD'S researches on the electric discharge III

" It is true that this assertion may appear incorrect to
many who may try the experiment under conditions which are
not quite favourable; excepting the one case in which, on
account of the exact equality of the two paths, no figure
appears. For it may happen that at first sight all the figures
appear to be positive under whatever conditions one works
and with either kind of electricity.

" The reason is simply that the complex negative figures in
this case belong to the class which already bear a strong positive
character, and can scarcely be recognised as negative even
after thorough experience of them.

" But the considerable difference in size which results from
a change of pole amply suffices to remove at once any doubt
respecting the real nature of the figures, and to show the
accordance between the experiments and the theoretical pre-
dictions.

" To sum up, the following results were obtained : —

" 1. If, after springing across a spark-gap, an electric dis-
charge has before it two paths to earth, one short and the
other long, and separated by a test -plate, the discharge -
current splits up, so long as the sparking distance is small.
But when it is larger the electricity rushes solely along the
shorter path, carrying with it out of the other branch elec-
tricity of the same sign

" 2. If a series of electric waves is sent along a wire which
is insulated at the end, the waves are reflected at the end, and
the phenomena which accompany this process in the case of
alternating discharges appear to be caused by interference
between the advancing and reflected waves.

" 3. An electric discharge traverses wires of equal lengths
in equal times, whatever may be the material of which these
wires consist"

ON AN EFFECT OF ULTRA-VIOLET LIGHT UPON
THE ELECTRIC DISCHARGE

{SUzungsberichte d. Berl. Akad. d, Wiss., June 9, 1887. WiedemanrCs

Ann, 31, p. 983.)

In a series of experiments on the effects of resonance between
very rapid electric oscillations which I have carried out and
recently published,^ two electric sparks were produced by the
same discharge of an induction-coil, and therefore simul-
taneously. One of these, the spark A, was the discharge-
spark of the induction-coil, and served to excite the primary
oscillation. The second, the spark B, belonged to the induced
or secondary oscillation. The latter was not very luminous ;
in the experiments its maximum length had to be accurately
measured. I occasionally enclosed the spark B in a dark
case so as more easily to make the observations ; and in so
doing I observed that the maximum spark -length became
decidedly smaller inside the case than it was before. On
removing in succession the various parts of the case, it was
seen that the only portion of it which exercised this pre-
judicial effect was that which screened the spark B from the
spark A. The partition on that side exhibited this effect, not
only when it was in the immediate neighbourhood of the spark
By but also when it was interposed at greater distances from
B between A and B, A phenomenon so remarkable called
for closer investigation. The following communication con-
tains the results which I have been able to establish in the
course of the investigation : —

1 See II., p. 29.

64 ON AN EFFECT OF ULTKA-VIOLET LIGHT iv

1. The phenomenon could not be traced to any screening
effect of an electrostatic or electromagnetic nature. For the
effect was not only exhibited by good conductors interposed
between A and B, but also by perfect non-conductors, in
particular by glass, paraf^, ebonite, which cannot possibly exert
any screening effect. Further, metal gratings of coarse texture
showed no effect, although they act as efficient screens.

2. The fact that both sparks A and B corresponded with
synchronous and very rapid oscillations was immaterial.
For the same effect could be exhibited by exciting two
simultaneous sparks in any other way. It also appeared
when, instead of the induced spark, I used a side-spark (this
term having the same significance as in my earlier paper).
It also appeared when I used as the spark B a side-discharge
(according to Eiess's terminology), such as is obtained by con-
necting one pole of an induction-coil with an insulated
conductor and introducing a spark-gap. But it can best and
most conveniently be exhibited by inserting in the same
circuit two induction-coils with a common interruptor, the
one coil giving the spark A and the other the spark B. This
arrangement was almost exclusively used in the subsequent
experiments. As I found the experiment succeed with a
number of different induction-coils, it could be carried out
with any pair of sets of apparatus at pleasure. At the same
time it will be convenient to describe the particular experi-
mental arrangement which gave the best results and was
most frequently used. The spark A was produced by a large
Euhmkorfif coil (a, Fig. 18), 52 cm. long and 20 cm. in
diameter, fed by six large Bunsen cells (6) and provided with
a separate mercury-break (c). With the current used it
could give sparks up to 10 cm. long between point and plate,
and up to about 3 cm. between two spheres. The spark
generally used was one of 1 cm. length between the points of
a common discharger (d). The spark B was produced by a
smaller coil (originally intended for medical use) of relatively
greater current-strength, but having a maximum spark-length
of only ^/g-l cm. As it was here introduced into the
circuit of the larger coil, its condenser did not come into
play, and thus it only gave sparks of 1 - 2 mm. length. The

UPON THE ELECTRIC DISCHARGE

^^1=

sparks used were ones about 1 mm. long between the nickel-
plated knobs of a Eiess spark-micrometer (/), or between
brass knobs of 5 to 10 cm.
diameter. When the appar-
atus thus arranged was set up
with both spark-gaps parallel
and not too far apart, the
interrupter set going, and the
spark-micrometer drawn out
just so far as to still permit
sparks to pass regularly, then
on placing a plate (p) of
metal, glass, etc., between the
two sparks-gaps d and /, the
sparks are extinguished im- Fig. is.

mediately and completely.
On removing the plate they immediately reappear.

3. The effect becomes more marked as the spark A is
brought nearer to the spark B, The distance between the two
sparks when I first observed the phenomenon was 1^ metres,
and the effect is, therefore, easily observed at this distance.
I have been able to detect indications of it up to a distance of
3 metres between the sparks. But at such distances the
phenomenon manifests itself only in the greater or less
regularity of the stream of sparks at -B ; at distances less than
a metre its strength can be measured by the difference
between the maximum spark-length before and after the
interposition of the plate. In order to indicate the magnitude
of the effect I give the following, naturally rough, observations
which were obtained with the experimental arrangement shown
in Fig. 18:—

Distance between
the Sparks in
cm.

50
40
30
20
10

Length of Spark JB in mm.
before and after insert-
ing the Plate.

Difference.

0-8

0-9

0-8

0-1

1-0

0-8

0-2

1-1

0-8

0-3

1-3

0-8

0-5

1-5

0-8

0-7

1-6

0-8

1-8

0-8

66 ON AN EFFECT OF ULTRA-VIOLET LIGHT iv

It will be seen that, under certain conditions, the sparking
distance is doubled by removing the plate.

4. The observations given in the table may also be
adduced as proofs of the following statement which the reader
will probably have assumed from the first. The phenomenon
does not depend upon any prejudicial eflfect of the plate on the
spark B, but upon its annulling a certain action of the spark
A, which tends to increase the sparking distance. When
the distance between the sparks A and B is great, if we so
adjust the spark -micrometer that sparks no longer pass at B,
and then bring the spark-micrometer nearer to A, the stream
of sparks in B reappears; this is the action. If we now
introduce the plate, the sparks are extinguished ; this is the
cessation of the action. Thus the plate only forms a means
of exhibiting conveniently and plainly the action of the spark
A, I shall in future call A the active spark and B the
passive spark.

5. The efficiency of the active spark is not confined to
any special form of it. Sparks between knobs, as well as
sparks between points, proved to be efficient Short straight
sparks, as well as long jagged ones, exhibited the eflfect. There
was no diflference of any importance between faintly luminous
bluish sparks and brilliant white ones. Even sparks 2 mm.
long made their influence felt to considerable distances. Nor
does the action proceed from any special part of the spark ;
every part is efifective. This statement can be verified by
drawing a glass tube over the spark-gap. The glass does not
allow the effect to pass through, and so the spark under these
conditions is inactive. But the eflfect reappears as soon as a
short bit of the spark is exposed at one pole or the other, or
in the middle. I have not observed any influence liiib to the
metal of the pole. And in arranging the experimgnt it is not
of importance that the active spark should be parallel to the
passive one.

6. On the other hand, the susceptibility of the passive
spark to the action is to a certain extent dependent upon its
form. I could detect no susceptibility with long jagged
sparks between points, and but little with short sparks

IV UPON THE ELECTRIC DISCHARGE 67

between points. The effect was best displayed by sparks
between knobs, and of these most strikingly by short
sparks. It is advisable to use for the experiments sparks
1 mm. long between knobs of 5-10 mm. diameter. Still
I have distinctly recognised the effect with sparks 2 cm. long.
Perhaps the absolute lengthening which such sparks experi-
ence is really as great as in the case of shorter sparks, but at
all events the relative increase in length is much smaller ; and
hence the effect disappears in the differences which occur
between' the single discharges of the coil. I have not dis-
covered any perceptible influence due to the material of the
pole. I examined sparks between poles of copper, brass, iron,
aluminium, tin, zinc, and lead. If there was any difference
between the metals with respect to the susceptibility of the
spark, it appeared to be slightly in favour of the iron. The
poles must be clean and smooth ; if they are dirty, or corroded
by long use, the effect is not produced.

7. The relation between the two sparks is reciprocal.
That is to say, not only does the larger and stronger
spark increase the spark-length of the smaller one, but con-
versely the smaller spark has the same effect upon the spark-
length of the larger one. For example, using the same
apparatus as before, let us adjust the spark -micrometer so
that the discharge in it passes over regularly ; but let the
discharger be so adjusted that the discharges of the large coil
just miss fire. On bringing the spark-micrometer nearer we
find that these discharges are again produced; but that on
introducing a plate the action ceases. For this purpose the
spark of the large coil must naturally be fairly sensitive ; and,
inasmuch as long sparks are less sensitive, the effect is not so
striking. If both coils are just at the limit of their sparking
distance complications arise which have probably no connection
with the matter at present under discussion.^ One frequently
has occasion to notice a long spark being started by other
ones which are much smaller, and in part this may certainly
be ascribed to the action which we are investigating. When
the discharge of a coil is made to take place between knobs,
and the knobs are drawn apart until the sparks cease, then it

^ [See Note 8 at end of book.]

68 ON AN EFFECT OF ULTRA-VIOLET LIGHT iv

is found that 'the sparking begins again when an insulated
conductor is brought near one of the knobs so as to draw
small side -sparks from it. I have proved to my entire
satisfaction that the side-discharges here perform the function
of an active spark in the sense of the present investigation.
It is even sufficient to touch one of the knobs with a non-
conductor, or to bring a point somewhat near it, in order to
give rise to the same action. It appears at least possible that
the function of an active spark is here performed by the
scarcely visible side-discharges over the. surface of the non-
conductor and of the point.

8. The effect of the active spark spreads out on aU sides
in straight lines and forms rays exactly in accordance with
the laws of the propagation of Ught. Suppose the axes of
both of the sparks used to be placed vertically, and let a plate
with a vertical edge be pushed gradually from the side in
between the sparks. It is then found that the effect of the
active spark is stopped, not gradually, but suddenly, and in a
definite position of the plate. If we now look along the edge of
the plate from the position of the passive spark, we find that
the active spark is just hid by the plate. If we adjust the
plate with its edge vertical between the two sparks and slowly
remove it sideways, the action begtos again in a definite
position, and we now find that, from the position of the
passive spark, the active spark has just become visible beyond
the edge of the plate. If we place between the sparks
a plate with a small vertical slit and move it backwards
and forwards, we find that the action is only transmitted
in one perfectly definite position, namely, when the active
spark is visible through the slit from the position of the
passive spark. If several plates with such slits are interposed
behind each other, we find that in one particular position the
action passes through tTie whole lot. If we seek these posi-
tions by trial, we end by finding (most easily, of course, by
looking through) that all the slits lie in the vertical plane
which passes through the two sparks. If at any distance
from the active spark we place a plate with an aperture of
any shape, and by moving the active spark about fix the
limits of the space within which the action is exerted, we

IV UPON THE ELECTKIC DISCHARGE 69

obtain as this limit a conical surface determined by the active
spark as apex and by the limits of the aperture. If we place
a small plate in any position in front of the active spark we
find, by moving the passive spark about, that the plate stops
the action of the active spark within exactly the space which
it shelters from its light. It scarcely requires to be explained
that the action is not only annulled in the shadows cast by
external bodies, but also in the shadows of the knobs of the
passive spark. In fact, if we turn the latter so that its axis
remains in the plane of the active spark, but is perpendicular
to it instead of being parallel, the action immediately ceases.

9. Most solid bodies hinder the action of the active spark,
but not all ; a few solid bodies are transparent to it. All the
metals which I tried proved to be opaque, even in thin sheets,
as did also paraffin, shellac, resin, ebonite, and india-rubber;
all kinds of coloured and uncoloured, polished and unpolished,
thick and thin glass, porcelain, and earthenware ; wood, paste-
board, and paper; ivory, horn, animal hides, and feathers;
lastly, agate, and, in a very remarkable manner, mica, even in
the thinnest possible flakes. Further investigation of crystals
showed variations from this behaviour. Some indeed were
equally opaque, e,g, copper sulphate, topaz, and amethyst ; but
others, such as crystallised sugar, alum, calc-spar, and rock-salt,
transmitted the action, although with diminished intensity;
finally, some proved to be completely transparent, such as
gypsum (selenite), and above all rock-crystal, which scarcely
interfered with the action even when in layers several centi-
metres thick. The following is a convenient method of test-
ing : — The passive spark is placed a few centimetres away from
the active spark, and is brought to its maximum length. The
body to be examined is now interposed. If this does not stop
the sparking the body is very transparent. But if the spark-
ing is stopped, the spark-gap must be shortened until it comes
again into action. An opaque substance is now interposed in
addition to the body under investigation. If this stops the
sparking once more, or weakens it, then the body must have
been at any rate partially transparent; but if the plate pro-
duces no further effect it must have been quite opaque. The
influence of the interposed bodies increases with their thickness.

70 ON AN EFFECT OF ULTRA-VIOLET LIGHT iv

and it may properly be described as an absorption of the
action of the active spark ; in general, however, even those
bodies which only act as partial absorbers, exert this influence
even in very thin layers.

10. Liquids also proved to be partly transparent and
partly opaque to the action. In order to experiment upon
them the active spark was brought about 10 cm. vertically
above the passive one, and between both was placed a glass
vessel, of which the bottom consisted of a circular plate of
rock-crystal 4 mm. thick. Into this vessel a layer, more or
less deep, of the liquid was poured, and its influence was then
estimated in the manner above described for solid bodies.
Water proved to be remarkably transparent ; even a depth of
5 cm. scarcely hindered the action. In thinner layers pure
concentrated sulphuric acid, alcohol, and ether were also trans-
parent. Pure hydrochloric acid, pure nitric acid, and solu-
tion of ammonia proved to be partially transparent. Molten
paraffin, benzole, petroleum, carbon bisulphide, solution of
ammonium sulphide, and strongly coloured liquids, e.g, solutions
of fuchsine, potassium permanganate, were nearly or completely
opaque. The experiments with salt solutions proved to be
interesting. A layer of water 1 cm. deep was introduced into
the rock-crystal vessel ; the concentrated salt solution was
added to this drop by drop, stirred, and the effect observed.
With many salts the addition of a few drops, or even a single
drop, was sufficient to extinguish the passive spark ; this was
the case with nitrate of mercury, sodium hyposulphite, potassium
bromide, and potassium iodide. When iron and copper salts
were added, the extinction of the passive spark occurred before
any distinct colouring of the water could be perceived. Solutions
of sal-ammoniac, zinc sulphate, and common salt ^ exercised an
absorption when added in larger quantities. On the other
hand, the sulphates of potassium, sodium, and magnesium were
very transparent even in concentrated solution.

11. It is clear from the experiments made in air that
some gases permit the transmission of the action even to con-

^ According to my experiments a concentrated solution of common salt is
a more powerful absorbent than crystallised rock-salt. This result is so remark-
able as to require confirmation.

IV UPON THE ELECTRIC DISCHARGE 71

siderable distances. Some gases, however, are very opaque to
it. In experimenting on gases a tube 20 cm. long and 2*5 cm.
in diameter was interposed between the active and passive
sparks; the ends of this tube were closed by thin quartz
plates, and by means of two side-tubes any gas could at will
i be led through it. A diaphragm prevented the transmission

1 of any action excepting through the glass tube. Between

hydrogen and air there was no noticeable difference. Nor
5 could any falling off in the action be perceived when the tube

f was filled with carbonic acid. But when coal-gas was intro-

duced, the sparking at the passive spark-gap immediately ceased.
When the coal-gas was driven out by air the sparking began
again; and this experiment could be repeated with perfect
regularity. Even the introduction of air with which some coal-
gas had been mixed hindered the transmission of the action.
Hence a much shorter stratum of coal-gas was sufficient to stop
the action. If a current of coal-gas 1 cm. in diameter is
allowed to flow freely into the air between the two sparks, a
shadow of it can be plainly perceived on the side remote from
the active spark, i.e. the action of this is more or less com-
pletely annulled. A powerful absorption like that of coal-gas is
exhibited by the brown vapours of nitrous oxide. With these,
again, it is not necessary to use the tube with quartz-plates
in order to show the action. On the other hand, although
chlorine and the vapours of bromine and iodine do exercise
absorption, it is not at all in proportion to their opacity. No
absorptive action could be recognised when bromine vapour
had been introduced into the tube in sufficient quantity to
produce a distinct coloration; and there was a partial trans-
mission of the action even when the bromine vapour was so
dense that the active spark (coloured a deep red) was only
just visible through the tube.

12. The intensity of the action increases when the air
around the passive spark is rarefied, at any rate up to a certain
point. The increase is here supposed to be measured by the
difference between the lengths of the protected and the unpro-
tected sparks. In these experiments the passive spark was
produced under the bell-jar of an air-pump between adjustable
poles which passed through the sides of the bell-jar. A window

72 ON AN EFFECT OF ULTRA-VIOLET LIGHT iv

of rock-crystal was inserted in the bell-jar, and through this the
action of the other spark had to pass. The maximum spark- I

length was now observed, first with the window open, and
then with the window closed; varying air-pressures being
used, but a constant current. The following table may be
regarded as typical of the results : —

Air-pressure in Length in mm. of Spark

mm. of with Window Difference.

Mercury. Closed. Open.

760 0-8 1-5 0-7

500 0-9 2-3 1-4

300 1-0 3-7 2*7

100 2-0 6-2 4-2

80 very great very great undetermined.

It will be seen that as the pressure diminishes, the length ^

of the spark which is not influenced only increases slowly ;
the length of the spark which is influenced increases more
rapidly, and so the difierence between the two becomes greater.
But at a certain pressure the blue glow-light (Glimmlickt)
spread over a considerable portion of the cathode, the sparking
distance became very great, the discharge altered its character,
and it was no longer possible to perceive any influence due to
the active spark.

13. The phenomenon is also exhibited when the sparking
takes place in other gases than air; and also when the two
sparks are produced in two difierent gases. In these experi-
ments the two sparks were produced in two small tubulated
glass vessels which were closed by plates of rock-crystal and
could be filled with different gases. The experiments were
tried mainly because certain circumstances led to the sup-
position that a spark in any given gas would only act upon
another spark in the same gas, and on this account the four
gases — hydrogen, air, carbonic acid, and coal-gas — ^were tried in
the sixteen possible combinations. The main conclusion arrived
at was that the above supposition was erroneous. It should, how-
ever, be added that although there is no great difierence in the
efl&ciency of sparks when employed as active sparks in difierent
gases, there is, on the other hand, a notable difference in their
susceptibility when employed as passive sparks. Other things
being equal, sparks in hydrogen experienced a perceptibly greater

IV UPON THE ELECTRIC DISCHASGE"^^ 73

increase in length than sparks in air, and these again about
double the increase of sparks in carbonic acid and coal-gas. It
is true that no allowance was made for absorption in these
experiments, for its effect was not known when they were carried
out; but it could only have been perceptible in the case of
coal-gas.

14. All parts of the passive spark do not share equally in
the action ; it takes place near the poles, more especially near
the negative pole.^ In order to show this, the passive spark is
made from 1 to 2 cm. long, so that the various parts of it can
be shaded separately. Shading the anode has but a slight
effect ; shading the cathode stops the greater part of the action.
But the verification of this fact is somewhat difficult, because
with long sparks there is a want of distinctness about the
phenomenon. In the case of short sparks (the parts of which
cannot be separately shaded) the statement can be illustrated
as follows : — The passive spark is placed parallel to the active
one and is turned to right and left from the parallel into the

'. perpendicular position until the action stops. It is found that

there is more play in one direction than in the other ; the
advantage betog in favour of that direction in which the
cathode is turned towards the active spark. Whether the
effect is produced entirely at the cathode, or only chiefly at
the cathode, I have not been able to decide with certainty.

15. The action of the active spark is reflected from most
: surfaces. From polished surfaces the reflection takes place

according to the laws of regular reflection of Ught. In the
preliminary experiments on reflection a glass tube, 50 cm.

^ long and 1 cm. in diameter, was used ; this tube was open at

both ends, and was pushed through a large sheet of cardboard.
The active spark was placed at one end so that its action

I could only pass the sheet by way of the tube. If the passive

spark was now moved about beyond the other end of the tube
it was affected when in the continuation of the tubular space

^ and then only ; but in this case a far more powerful action

was exhibited than when the tube was removed and only the
diaphragm retained. It was this latter phenomenon that sug-

u gested the use of the tube ; of itself it indicates a reflection from

^ [See Note 9 at end of book.]

74 ON AJf EFFECT OF ULTRA-VIOLET LIGHT iv

the walls of the tube. The spark-micrometer was now placed
to one side of the beam proceeding out of the tube, and was so
disposed that the axis of the spark was parallel to the direction
of the beam. The micrometer was now adjusted so that the
sparking just ceased ; it was found to begin again if a plane
surface inclined at an angle of 45° to the beam was held in it
so as to direct the beam, according to the usual law of reflec-
tion, upon the passive spark. Eeflection took place more or
less from glass, crystals, and metals, even when these were not
particularly smooth; also from such substances as porcelain,
polished wood, and white paper. I obtained no reflection from a
well-smoked glass plate.

In the more accurate experiments the active spark was
placed in a vertical straight line ; at a little distance from it
was a largeish plate with a vertical slit, behind which could be
placed polished plane mirrors of glass, rock-crystal, and various
metals. The limits of the space within which the action was
exerted behind the slit were then determined by moving the
passive spark about. These limits were quite sharp and always
coincided with the limits of the space within which the image
of the active spark in the mirror was visible. On account of
the feebleness of the action these experiments could not be
carried out with unpolished bodies ; such bodies may be sup-
posed to give rise to diffused reflection.

16. In passing from air into a solid transparent medium
the action of the active spark exhibits a refraction like that of
light ; but it is more strongly refracted than visible light. The
glass tube used in the reflection experiments served here again
for the rougher experiments. The passive spark was placed in
the beam proceeding out of the tube and at a distance of
about 30 cm. from the end farthest from the active spark;
immediately behind the opening a quartz-prism was pushed
sideways into the beam with its refracting edge foremost. In
spite of the transparency of quartz, the effect upon the passive
spark ceased as soon as the prism covered the end of the tube.
If the spark was then moved in a circle about the prism in the
direction in which light would be refracted by the prism, it
was soon found that there were places at which the effect was
again produced. Now let the passive spark be fixed in the

UPON THE ELECTRIC DISCHARGE

position in which the effect is most powerfully exhibited ; o^
looking from this point towards the tube through the prism
the inside of the tube and the active spark at the end of it
cannot be perceived ; in order to see the active spark through
the tube the eye must be shifted backwards through a consider-
able distance towards the original position of the spark. The
same result is obtained when a rock-salt prism is used. In
the more accurate experiments the active spark was again fixed
vertically ; at some distance from it was placed a vertical slit,
and behind this a prism. By inserting a Leyden jar the active
spark could be made luminous, and the space thus illuminated

Fig. 19,

behind the prism could easily be determined. With the aid
of the passive spark it was possible to mark out the limits of
the space within which was exerted the action here under
investigation. Fig. 19 gives (to a scale of ^) the result thus
obtained by direct experiment. The space abed is filled
with light ; the space a' 6' </ d! is permeated by the action
which we are considering. Since the limits of this latter space
were not sharp, the rays a! V and c' d' were fixed in the follow-
ing way : — The passive spark was placed in a somewhat distant
position, about c', at the edge of the tract within which the
action was exerted. A screen m n (Fig. 19) with vertical edge
was then pushed in sideways until it stopped the action. The

76 ON AN EFFECT OF ULTRA-VIOLET LIGHT iv

position m of its edge then gave one point of the ray d dl. In
another experiment a prism of small refracting angle was used,
and the width of the slit was made as small, and the spark
placed as far from it as would still allow of the action being
perceived. The visible light was then spread out into a short
spectrum, and the influence of the active spark was found to
be exerted within a comparatively limited region which corre-
sponded to a deviation decidedly greater than that of the
visible violet Fig. 20 shows the positions of the rays as they
were directly drawn where the prism was placed, r being the
direction of the red, v of the violet, and w the direction in
which the influence of the active spark was most powerfully
exerted.

Pig. 20.

I have not been able to decide whether any double refrac-
tion of the action takes place. My quartz-prisms would not
permit of a suflScient separation of the beams, and the pieces of
calc-spar which I possessed proved to be too opaque.^

1 7. After what has now been stated, it will be agreed (at
any rate until the contrary is proved) that the light of the
active spark must be regarded as the prime cause of the action
which proceeds from it. Every other conjecture which is based
on known facts is contradicted by one or other of the experi-
ments. And if the observed phenomenon is an effect of light
at all it must, according to the results of the refraction-experi-
ments, be solely an efifect of the ultra-violet light. That it is
not an effect of the visible parts of the light is shown by the
fact that glass and mica are opaque to it, while they are trans-
parent to these. On the other hand, the absorption-experi-
ments of themselves make it probable that the effect is due to
ultra-violet light. Water, rock-crystal, and the sulphates of
the alkalies are remarkably transparent to ultra-violet light and
to the action here investigated ; benzole and allied substances

^ [See Note 10 at end of book.]

IV UPON THE ELECTRIC DISCHARGE 77

are strikingly opaque to both. Again, the active rays in
our experiments appear to lie at the outermost limits of
the known spectrum. The spectrum of the spark when
received on a sensitive dry -plate scarcely extended to the
place at which the most powerful effect upon the passive spark
was produced. And, photographically, there was scarcely any
difference between light which had, and light which had not,
passed through coal-gas, whereas the difference in the effect
upon the spark was very marked. Fig. 21 shows the extent
of some of the spectra taken. In a the
position of the visible red is indicated by r,
that of the visible violet by v, and that of
the strongest effect upon the passive spark
by w. The rest of the series give the photo-
graphic impressions produced — h after simply
passing through air and quartz, c after ^.^ ^i.

passing through coal-gas, d after passing
through a thin plate of mica, and e after passing through glass.

18. Our supposition that this effect is to be attributed to
light is confirmed by the fact that the same effect can be pro-
duced by a number of common sources of light. It is true
that the power of the light, in the ordinary sense of the word,
forms no measure of its activity as here considered ; and for the
purpose of our experiments the faintly visible light of the spark
of the induction-coil remains the most powerful source of light.
Let sparks from any induction-coil pass between knobs, and let
the knobs be drawn so far apart that the sparks fail to pass ;
if now the flame of a candle be brought near (about 8 cm. off)
the sparking begins again. The effect might at first be attri-
buted to the hot air from the flame ; but when it is observed
that the insertion of a thin small plate of mica stops the action,
whereas a much larger plate of quartz does not stop it, we are
compelled to recognise here again the same effect. The flames
of gas, wood, benzene, etc., all act in the same way. The non-
luminous flames of alcohol and of the Bunsen burner exhibit
the same effect, and in the case of the candle-flame the action
seems to proceed more from the lower, non-luminous part than
from the upper and luminous part. From a small hydrogen
flame scarcely any effect could be obtained. The light from

78 ON AN EFFECT OF ULTRA-VIOLET LIGHT iv

platinum glowing at a white-heat in a flame, or through the
action of an electric current, a powerful phosphorus flame burn-
ing quite near the spark, and burning sodium and potassium, all
proved to be inactive. So also was burning sulphur ; but this
can only have been on account of the feebleness of the flame,
for the flame of burning carbon bisulphide produced some
efiect Magnesium L'ght produced a far more powerful effect
than any of the above sources ; its action extended to a distance
of about a metre. The limelight, produced by means of coal-
gas and oxygen, was somewhat weaker, and acted up to a dis-
tance of half a metre ; the action was mainly due to the jet
itself: it made no great difierence whether the lime-cylinder
was brought into the flame or not. On no occasion did I
obtain a decisive effect from sunlight at any time of the day
or year at which I was able to test it. When the sunlight was
concentrated by means of a quartz lens upon the spark there
was a slight action; but this was obtained equally when a
glass lens was used, and must therefore be attributed to the
heating. But of all sources of light the electric arc is by far
the most effective ; it is the only one that can compete with
the spark. If the knobs of an induction-coil are drawn so far
apart that sparks no longer pass, and if an arc light is started
at a distance of 1, 2, 3, or even 4 metres, the sparking begins
again simultaneously, and stops again when the arc light goes
out. By means of a narrow opening held in front of the arc
light we can separate the violet light of the feebly luminous
arc proper from that of the glowing carbons ; and we then find
that the action proceeds chiefly from the former. With the
light of the electric arc I have repeated most of the experi-
ments already described, e.g. the experiments on the recti-
linear propagation, reflection, and refraction of the action,
as well as its absorption by glass, mica, coal-gas, and other
substances.

According to the results of our experiments, ultra-violet
light has the property of increasing the sparking distance of
the discharge of an induction-coil, and of other discharges.
The conditions under which it exerts its effect upon such dis-
charges are certainly very complicated, and it is desirable that
the action should be studied under simpler conditions, and
especially without using an induction-coil. In endeavouring

IV UPON THE ELECTiaC DISCHARGE 79

to make progress in this direction I have met with diffi-
culties.^ Hence I confine myself at present to communicating
the results obtained, without attempting any theory respecting
the manner in which the observed phenomena are brought
about.

^ [See Note 11 at end of book.]

■Ik

ON THE ACTION OF A RECTILINEAR ELECTRIC OSCIL-
LATION UPON A NEIGHBOURING CIRCUIT

{ Wiedemann* s Annalen, 34, p. 155, 1888.)

In an earlier paper ^ I have shown how we may excite in
a rectilinear unclosed conductor the fundamental electric oscil-
lation which is proper to this conductor. I have also shown
that such an oscillation exerts a very powerful inductive effect
upon a nearly closed circuit in its neighbourhood, provided that
the period of oscillation of the latter is the same as that of the
primary oscillation. As I intended to make use of these effects
in further researches, I examined the phenomenon in all the
various positions which the secondary circuit could occupy with
reference to the inducing current. The total inductive action
of a current-element upon a closed circuit can be completely
calculated by the ordinary methods of electromagnetics. Now
since our secondary circuit is closed, with the exception of an
exceedingly short spark-gap, I supposed that this total action
would suffice to explain the new phenomena ; but I found that
in this I was mistaken. In order to arrive at a proper under-
standing of the experimental results (which are not quite
simple), it is necessary to regard the secondary circuit also as
being in every respect unclosed. Hence it is not sufficient to pay
attention to the integral force of induction ; we must take into
consideration the distribution of the electromagnetic force along
the various parts of the circuit: nor must the electrostatic
force which proceeds from the charged ends of the oscillator
be neglected. The reason of this is the rapidity with which

1 See II., p. 29.

V-

V RECTILINEAR ELECTRIC OSCILLATION 81

the forces in these experiments alter their sign. A slowly
alternating electrostatic force would excite no sparks in our
secondary conductor, even if its intensity were very great,
since the free electricity of the conductor could distribute
itself, and would distribute itself, in such a way as to neutralise
the effect of the external force ; but in our experiments the
direction of the force alters so rapidly that the electricity has
no time to distribute itself in this way.

For the sake of convenience I will first sketch the theory
and then describe the phenomena in connection with it. It
would indeed be more logical to adopt the opposite course;
for the facts here communicated are true independently of the
theory, and the theory here developed depends for its support
more upon the facts than upon the explanations which accom-
pany it.

The Apparatvs

Before we proceed to develop the theory, we may briefly
describe the apparatus with which the experiments were carried
out, and to which the theory more especially relates. The
primary conductor consisted of a straight copper wire 5 mm.
in diameter, to the ends of which were attached spheres 30
cm. in diameter made of sheet-zinc. The centres of these
latter were 1 metre apart The wire was interrupted in the
middle by a spark-gap ^j ^ cm. long; in this oscillations were
excited by means of the most powerful discharges which
could be obtained from a large induction-coil. The direction
of the wire was horizontal, and the experiments were carried
out only in the neighbourhood of the horizontal plane passing
through the wire. This, however, in no way restricts the
general nature of the experiments, for the results must be the
same in any meridional plane through the wire. The secondary
circuit, made of wire 2 mm. thick, had the form of a circle of
35 cm. radius which was closed with the exception of a short
spark-gap (adjustable by means of a micrometer-screw). The
change from the form used in the earlier experiments to the
circular form was made for the following reason. Even the
first experiments had shown that the spark -length was
different at different points of the secondary conductor,
even when the position of the conductor as a whole was not

82 ON THE ACTION OF A RECTILINEAR ELECTRIC v

altered. Now the choice of the circular form made it easily
possible to bring the spark-gap to any desired position. This
was most conveniently done by mounting the circle so that it
could be rotated about an axis passing through its centre, and
perpendicular to its plane. This axis was mounted upon
various wooden stands in whatever way proved from time to
time most convenient for the experiments.

With the dimensions thus chosen, the secondary circuit was
very nearly in resonance with the primary. It was tuned
more exactly by soldering on small pieces of sheet-metal to
the poles so as to increase the capacity, and increasing or
diminishing the size of these until a maximum spark-length
was attained.

Analysis of the Forces acting on the Secondary Circuit

We shall assume that the electric force at every point varies
as a simple periodic function of the time, changing its sense
without changing its direction ; we shall further assume that this
variation has the same phase at all points. This is true at any
rate in the neighbourhood of the primary conductor ; and for the
present we shall restrict our attention to points which lie near
it. Any point on the secondary circuit is determined by its
distance s measured from the spark-gap along the circle. We
denote by 2 the component of the electric force which acts at
any moment at the point s in the direction of the element d s
of the circle. Then 2 is a function of s which, after passing
round the whole circumference S, returns to its original value.
2 can therefore be developed in circular functions, beginning
thus —

2 = A + Bcos27rs/S+ . . . + B' sin 27rs/S + . . .

We shall neglect the higher terms. The effect of this will
be that our results will only be approximately correct; in
especial, weak sparks will be found to occur at places where
our calculations indicate that the sparking should disappear.*
But for the present our experiments are not sufficiently accu-
rate to justify us in paying any attention to these higher
terms. Let us therefore consider more closely the terms
which have been referred to.

V OSCILLATION UPON A NEIGHBOURING CIRCUIT 83

In the first place, the force A acts in the same sense, and
is of the same magnitude at all parts of the circle. A is inde-
pendent of the electrostatic force ; for the integral of the latter,
taken all round the circuit, is zero. A corresponds to the total
induced electromotive force. We know that this is measured
by the change, per unit of time, in the number of magnetic
lines of force which pass through the circla If we regard the
magnetic field in which the circle lies as being homogeneous,
A will be proportional to the component of the magnetic force
perpendicular to the plane of the secondary circuit. A will
therefore vanish when the direction of the magnetic force lies
in the plane of the secondary circuit. The force A gives rise
to an oscillation the intensity of which is independent of the
position of the spark-gap in the circle ; we shall denote by a
the spark-length which corresponds to this oscillation.

Turning now to the two other terms, we note, in the first
place, that the force B' sin 27rs/S is not in a position to
excite the fundamental oscillation of our circle. For it is
completely symmetrical on both sides of the spark-gap; it
acts in the same sense upon both poles, and therefore cannot
produce any difference between them. The force B cos 27r5/S
behaves otherwise. If we start from the spark-gap and
divide the circle into four equal parts, we find that this force
acts in the same direction in the two parts which lie opposite
the spark-gap, and that here it powerfully excites the funda-
mental oscillation. It is true that B acts in an opposite
direction in those part^ which lie nearest the spark-gap;
but the latter parts cannot here exert as powerful an
efifect. For since the current at the open ends of the circle
must always be zero, the electricity cannot move with the
same freedom near these ends as in the middle of the circle.
To elucidate the meaning of this somewhat brief statement we
may take as an illustration a string stretched between two
fixed points. If the middle and outer parts of the string are
acted upon by forces in opposite directions, the string as a
whole will move as if acted upon by the former set of forces,
and the fundamental note of the string will be produced if the
alternations of these forces synchronise with this note. Thus
the term B cos 27rs/S will excite the fundamental oscilla-
tion of our circle, and the direction of the oscillation will be

84 ON THE ACTION OF A RECTILINEAE ELECTRIC V

the same as if the force in the parts opposite the spark-gap
were alone effective. Further, the intensity of the oscillation
will be proportional to the quantity B. To find out what
this quantity means, let us assume that the electric field in
which the circle lies is approximately homogeneous. Let E
denote the total electric force acting in this field, cd the angle
which its direction makes with the plane of the secondary
circle, and the angle which the projection of the force upon
this plane makes with the straight line drawn from the
centre to the spark-gap. Then X = E cos © sin (27r5/S — 6)
approximately,^ and therefore B=— Ecoswsinft Hence
the value of B depends directly upon the total force ; electro-
static as well as electromagnetic causes contribute towards it.
B becomes zero when ci) = 90°, i.e, when the total force is
perpendicular to the plane of the circle ; and in this case it
will be zero for all positions of the spark-gap in the circle.
But B also becomes zero when ^ = 0, i.e. when the projec-
tion of the total force upon the plane oiF the circle coiucides
with the line drawn from the centre to the spark-gap. If in any
given position of the circle we suppose the spark-gap to move
round it, the angle 6 alters, and corresponding alterations are
produced in the value of B, in the intensity of the oscillation,
and in the spark-length. Thus the spark-length, which corre-
sponds to the second term of our series, can be approximately
represented by the expression ^ sin 6,

The two terms which produce respectively the spark-
lengths a and ^ sin have always the same phase. Hence
the induced oscillations have also the same phase, and their
amplitudes have to be added together. Now inasmuch as the
spark -lengths .are approximately proportional to the total
amplitudes, it follows that the spark-lengths have also to be
added together. If in any given position of the circle we
suppose the spark-gap to move round it, the spark-length
must accordingly be represented by an expression of the form
a -h /3 sin 6, Equal absolute values of this expression indi-
cate equal spark-lengths, whatever the sign may be ; for there
is nothing in the spark-length which corresponds to direction of

^ If the field is really homogeneous, then A=0 ; and A will therefore be small
when the field is approximately homogeneous. Nevertheless the force A may
give rise to an oscillation of the same order of magnitude as that produced by the
force B cos 27r5/S,

V OSCILLATION UPON A NEIGHBOURING CIRCUIT 85

oscillation. The absolute values of a and ^ could only be
determined by a much more detailed development of the theory ;
but we have indicated the conditions upon which they depend,
and this will be enough to enable us to understand the
phenomena.

The Plane of the SecoTidary Circuit is Verticcd

Let us now place our circle anywhere in the neighbourhood
of the primary conductor, with its plane vertical and its centre
in the horizontal plane which passes through the primary con-
ductor. As long as the spark-gap lies in the horizontal plane,
either on the one side or the other, we observe no sparks ;
but in other positions of the spark-gap we perceive sparks of
greater or less length. The disappearance of the sparks occurs
at two diametrically opposite points ; it follows that the a of
our formula is here always zero, and that becomes zero
when the spark-gap lies in the horizontal plane. From this
we draw the following conclusions : — In the first place, that
the lines of magnetic force in the horizontal plane are every-
where vertical, and therefore form circles around the primary
oscillation, as indeed is required by theory. Secondly, that
at all points of the horizontal plane the lines of electric force
lie in this plane itself, and therefore, that everywhere in space
they lie in planes passing through the primary oscillation —
which is also required by theory. If while the circle is in any
one of the positions here considered, we turn it about its axis
so as to remove the spark-gap out of the horizontal plane, the
spark-length increases until the sparks arrive at the top or
the bottom of the circle, in which positions they attain a
length of 2-3 mm. It can be proved in various ways that
the sparks thus produced correspond, as our theory requires,
to the fundamental oscillation of our circle, and not, as might
be suspected, to the first overtone. By making small altera-
tions in the circle, for example, we can show that the oscilla-
tion which produces these sparks is in resonance with the
primary oscillation ; and this would not hold for the overtones.
Again, the sparks disappear when the circle is cut at the
points where it intersects the horizontal plane, although these
points are nodes with respect to the first overtone.

ON THE ACTION OF A RECTILINEAR ELECTRIC

If we now maintain the spark-gap at the highest point and
turn the circle round about a vertical axis passing through its
centre and the spark-gap, we find that during a complete
revolution the sparks twice reach a maximum length and twice
become zero or else very nearly disappear. Clearly the maxi-
mum positions are those in which the direction of the electric
force lies in the plane of the circle (© = 0) ; whereas the
minimum positions are those in which the direction of the
electric force is perpendicular to this plane (cr) = 90°). Hence
we now have a means of finding out the direction of the
electric force at any point. I have investigated at a number
of points the positions in which the sparks either become very
short or completely disappear. In the lower part of Fig. 22

Fig. 22.

these are shown as taken directly from the experimental re-
sults. A A' is the primary conductor. The straight lines m n
are the projections of the secondary conductor on the horizon-
tal plane ; but all the observed positions are not shown in the
illustration. The short lines, normal to the lines m n, indicate
the direction of the force. Since this force nowhere becomes
zero, as we pass from the sphere A to the sphere A', it does
not change its sign. Hence we may furnish these normals
with arrow-heads, as has been done in the figure. With
regard to this figure we remark : —

. 1. The distribution of the total force in the neighbourhood
of the rectilinear oscillation is very similar to the distribution
of the electrostatic force which proceeds from the ends of the

V OSCILLATION UPON A NEIGHBOUBING CIBCUIT 87

oscillation. Near the centre of the oscillation in especial the
direction of the total force coincides with that of the electro-
static force ; the opposing electromagnetic force must therefore
be overpowered. Theory also indicates that in this neighbour-
hood the force of electromagnetic induction should be weaker
than the electrostatic force.

2. Still we can quite easily recognise the effect of the
electromagnetic induction. For the lines of force appear to a
certain extent to be pushed away from the axis of the oscilla-
tion ; in going from A to A^ they make a wider circuit than
they would if the electrostatic force alone were in operation.^
The explanation of this is that the force of induction weakens
the components of the electrostatic force which are parallel to
the primary conductor, whereas they are without influence
upon the components which are perpendicular to the primary
conductor.

The Plane of the Secondary Circle is Horizontal

We shall explain by reference to the upper half of Fig.
22 the phenomena which are observed when the plane of the
secondary circle is horizontal. First suppose the circle to be
brought into position /, in which its centre lies on the pro-
longation of the primary oscillation. After what has been
already stated, we may at once conclude from purely geometri-
cal considerations that the sparks will disappear when the
spark-gap is at the points b^ and b\ ; and also that maximum and
equal spark-lengths should be observed at the points a^ and a'^}
In my experiments the lengths of these sparks were 2*5 mm.

Now let us shift the circle sideways into the position
//. Here lines of magnetic force pass through the circle. The
integral of the force of induction taken round the circle does
not vanish ; a is not zero. We may therefore expect to find
that our expression a -(- ^8 sin ^, in which the value of a at
first is small, will have (since we pay no regard to sign) two
maxima of unequal value, viz. fi + a and ^ — a. These will
occur when ^ = 90°, and the line joining them will be per-
pendicular to the direction of the electric force. These two
maxima must be separated by two points at which no sparking

^ The original drawing showed this more plainly than the reduced copy does.

88 ON THE ACTION OF A BECTILINEAK ELECTRIC v

occurs, and these points should lie near the smaller maxi-
mum. This agrees with the experimental results. For in the
points &2 ^^^ ^'2 ^^ again find our null-points which have
been drawn closer together ; between these at a^ and a'^ are
maximum spark-lengths, and that at a^ is found to be 3*5
mm., while that at a'g is 2 mm. The line ^2 ^'2 ^s very nearly
perpendicular to the direction of the electric force. In order to
complete our explanation we have yet to show that a2 must
correspond to the sum, and a'g to the difference of the actions.
Let us consider the case in which the spark-gap lies at a2-
While the sphere A is positively charged, the total electric
force in those parts of the circle which lie opposite to 0^2 urges
positive electricity in a direction away from A; it tends to
move positive electricity in a circular direction, which in the
case of our illustration would be the direction of the hands of
a clock. Between the spheres A and A^ the electrostatic force
at the same time is directed from A towards A' ; the force of
induction which is always opposed to it is therefore, in the
neighbourhood of the conductor, directed towards A, and every-
where in space is parallel to this direction. Now since this
force in our circle acts more strongly in the neighbourhood of
the primary oscillation than it does at a distance from the latter,
it follows that this force also tends to set positive electricity in
motion in a circular direction corresponding to that of the
hands of a clock. Hence at a^ both causes act in the same
sense and so strengthen each other. Similarly it can be shown
that at a'2 ^^®y ^ct in opposite senses and weaken each other.
Thus the phenomenon is completely explained.

Now suppose our circle to be moved nearer the centre
of the primary oscillation to ///. Here the two points at
which the spark is extinguished coincide into one. One maxi-
mum disappears; and opposite to a very extended tract of
extinction a'3 lies the second maximum with a spark-length of
4 mm. Here evidently a = yS, and the spark-length is repre-
sented by the formula a(l -hsin 6). The line a^ a\ is again
perpendicular to the direction of the electric force. If we move
the circle still nearer to the centre of the primary oscilla-
tion, a becomes greater than ^. The expression a^ ^ smO
can no longer be zero for any value of 6, but it oscillates
between a maximum value a + ^ and a minimum value a — yS.

V OSCILLATION UPON A NEIGHBOURING CIRCUIT 89

Experiment also shows that in the positions under considera-
tion there are no longer any points at which the sparks
are extinguished; there are only maxima and minima. In
position IV we have at a^ a spark-length of 5*5 mm., and at
a'^ a length of 1*5 mm. In position Fwe have at a^ a spark-
length of 6 mm., at a'g the spark-length is 2*5 mm.,^ and at
intermediate points we have intermediate values. In passing
over from position III to position V, the join aa^ turns sharply
from a direction parallel to the primary current into a
direction perpendicular to it; it therefore always remains
approximately perpendicular to the direction of the electric
force.

In the last-mentioned positions the sparks are mainly due
to electromagnetic induction. Hence, in my first paper, I made
no error in speaking of the phenomena in these positions as
being electromagnetic effects. Nevertheless, the production of
sparks even in these positions is completely independent of
electrostatic causes only when we bring the spark-gap into the
mean position between maximum and minimum, in which par-
ticular position ^ sin becomes zero.

The Remaining Positions of the Secondary Circle

The positions which as yet have not been discussed, and in
which the secondary circle is inclined to the horizontal plane,
can be regarded as intermediate states between those which
have already been described. In all such cases I have found
the theory confirmed and have noticed no phenomenon which
did not fit in with it. Let us consider one case only. Suppose
the circle in the first place to lie in the horizontal plane and
in position V, with the spark-gap turned towards the primary
oscillation at a^, Now let the circle be turned about a hori-
zontal axis passing through its centre parallel to the primary
oscillation, in such a way that the spark-gap rises. While
the circle turns, the electric force is always at right angles to
the straight line drawn from its centre to the spark-gap ; thus
is always equal to 90°. The value of ^ is approximately
constant in all positions. But a varies approximately as the

^ In these positions the secondary spark must, in order to avoid disturbing
causes, be protected from the light of the primary spark.

90 ON THE ACTION OF A RECTILINEAR ELECTRIC v

cosine of the angle <f> between the plane of the circle and the
horizontal plane, since a is proportional to the number of lines
of magnetic force cut by the circle. Thus if a^ denote the
value of a in the initial position, the value of a in any other
position is a^ cos ^, and it may therefore be expected that the
relation between the spark-length and the angle <f> may be
given by the expression a^ cos ^+^8, where ao> ^. Experi-
ment confirms this. For as we raise the spark-gap the spark-
ing distance steadily decreases from its initial value of 6 mm.
and acquires at the highest point in its circuit a length of 2
mm. It then sinks farther in the second quadrant almost to
zero, increases again to the smaller maximum of 2*5 mm.,
which occurs in the horizontal plane, again decreases, and after
passing through the same stages in the reverse order it returns
to its original value.

Let us suppose that in the course of the movements above
described we hold the circle in the position in which the
spark-gap is at its highest point. If now we raise the circle
vertically as a whole, the sparks became weaker and ultimately
they almost disappear; if we lower the circle vertically the
sparking becomes more vigorous. But if under similar circum-
stances the spark-gap is at its lowest point, the effects are
reversed. These results may be deduced by purely geometri-
cal reasoning from what has been already stated.

ITie Forces at Greater Distances

We have already mentioned a method of ascertaining
experimentally the direction of the total electric force at any
point. There was no diflBculty in extending the application
of this method to greater distances, and there was all the
more reason for making the experiment because the existing
theories of electromagnetics differ widely in t^eir views as to
the distribution of the force in the neighbourhood of an un-
closed current. We therefore place the plane of our circle
in a vertical position, bring the spark-gap to the highest point,
and by turning the circle about a vertical axis we try to ascer-
tain in what position the sparks are longest and in what
position they disappear or nearly disappear. But when we
get to a distance of 1-1*5 metre from the primary oscillation,

V OSCILLATION UPON A NEIGHBOURING CIRCUIT 91

we are met by an unexpected difficulty. For the maxima and
minima lose their distinctness, except in particular positions, so
that it becomes difficult to adjust the position of the circle for
either; indeed, at certain places the differences between the
spark-lengths during a revolution of the circle are so small that
it becomes impossible to specify any definite direction of the force.
Now observe that this difficulty again disappears when we pass
beyond a distance of about 2 metres. Certainly the sparks
are now very small and need to be observed in the dark and
with the aid of a lens; but they disappear sharply in a
definite position of the circle, and are strongest in a position at
right angles to this. When the distance is further increased
the spark-length only diminishes slowly. I have not been
able to decide the farthest distance at which they could be
observed. When I placed the primary conductor in one
comer of a large lecture-room 14 metres long and 12 metres
broad, the sparks could be perceived in the farthest parts of
the room ; the whole room seemed filled with the oscillations
of the electric force. It is true that in the neighbouring
rooms the action could not be perceived even at small dis-
tances ; solid walls exercise a powerful damping effect upon it.
In the lecture-room referred to I ascertained the distribution
of the force as follows : — Wherever the direction of the force
could be definitely determined I marked it by a chalk line on
the floor; but wherever it could not well be determined I

drew a star upon the floor. Fig. 23 .

shows on a reduced scale a portion ___

of the diagram thus made; with

reference to it we note : — ^ _ _

1. At distances beyond 3 metres ^ zi ^ ^
the force is everywhere parallel to ^^i/^/^^^
the primary oscillation. This is ^^^^^^
clearly the region in which the C Z -~ <^ ^

electrostatic force has become negli- ^ Z. —

gible, and the electromagnetic force Fig. 23.

alone is effective. AU theories agree

in this — that the electromagnetic force of a current-element is
inversely proportional to the distance, whereas the electrostatic
force (as the difference between the effects of the two poles)
is inversely proportional to the third power of the distance.

92 ON THE ACTION OF A RECTILINEAR ELECTRIC v

It is worthy of notice that, in the direction of the oscillation,
the action becomes weaker much more rapidly than in the
perpendicular direction, so that in the former direction the
effect can scarcely be perceived at a distance of 4 metres,
whereas in the latter direction it extends at any rate farther
than 12 metres. Many of the elementary laws of induction
which are accepted as possible will have to be abandoned
if tested by their accordance with the results of these ex-
periments.

2. As already stated, at distances less than a metre the
character of the distribution is determined by the electrostatic
force.

3. Along one pair of straight lines the direction of the
force can be determined at every point. The first of these
straight lines is the direotion of the primary oscillation itself ;
the second is perpendicular to the primary osciUation through
its centre. Along the latter the magnitude of the force is at
no point zero ; the size of the sparks induced by it diminishes
steadily from greater to smaller values. In this respect also
the phenomena contradict certain of the possible elementary
laws which require that the force should vanish at a certain
distance.

4. One remarkable fact that results from the experiment
is, that there exist regions in which the direction of the force
cannot be determined ; in our diagram each of these is indi-
cated by a star. These regions form in space two rings
around the rectilinear oscillation. The force here is of
approximately the same strength in all directions, and yet it
cannot act simultaneously in these diflferent directions ; hence
it must assume in succession these diflferent directions. Hence
the phenomenon can scarcely be explained otherwise than as
follows : — The force does not retain the same direction and
alter its magnitude ; its magnitude remains approximately con-
stant, while its direction changes, passing during each osciUation
round all the points of the compass. I have not succeeded
in finding an explanation of this behaviour, either in the
terms which have been neglected in our simplified theory, or in
the harmonics which are very possibly mingled with our fun-
damental vibration. And it seems to me that none of the
theories which are based upon the supposition of direct action-

latioH,
n tit
1 ih

ctioE

ei-

tie
atic

tie
3se
If:

V OSCILLATION UPON A NEIGHBOURING CIRCUIT 93

at-a-distance would lead us to expect anything of this kind.
But the phenomenon is easily explained if we admit that the
electrostatic force and the electromagnetic force are propagated
with different velocities. For in the regions referred to these
two forces are perpendicular to one another, and are of the
same order of magnitude ; hence if an appreciable difference
of phase has arisen between them during the course of their
journey, their resultant — the total force — will, during each
oscillation, move round all points of the compass without
approaching zero in any position.

A difference between the rates of propagation of the
electrostatic and electromagnetic forces implies a finite rate
of propagation for at least one of them. Thus it seems to
me that we probably have before us here the first indication
of a finite rate of propagation of electrical actions.

In an earlier paper ^ I mentioned that trivial details, with-
out any apparent reason, often interfered with the production
of oscillations by the primary spark. One of these, at any
^ rate, I have succeeded in tracing to its source. For I find
^ that when the primary spark is illuminated, it loses its power
of exciting rapid electric disturbances. Thus, if we watch
the sparks induced in a secondary conductor, or in any
auxiliary conductor attached to the discharging circuit, we see
that these sparks vanish as soon as a piece of magnesium wire
is lit, or an arc light started, in the neighbourhood of the
primary spark. At the same time the primary spark loses its
crackling sound. The spark is particularly sensitive to the
light from a second discharge. Thus the oscillations always
cease if we draw sparks from the opposing faces of the knobs
by means of a small insulated conductor; and this even
though these sparks may not be visible. In fact, if we only
bring a fine point near the spark, or touch any part of the
inner surfaces of the knobs with a rod of sealing-wax or glass,
or a slip of mica, the nature of the spark is changed, and the
oscillations cease. Some experiments made on this matter
seem to me to prove (and further experiments will doubtless
confirm this) that in these latter cases as well the effective

^ See No. II., p. 29.

94 RECTILINEAR ELECTRIC OSCILLATION v

cause of the change is the light of a side-flash, which is
scarcely visible to the eye.

These phenomena are clearly a special form of that action
of light upon the electric discharge, of which one form was
first described by myself some time ago, and which has since
been studied in other forms by Herren E. Wiedemann, H.
Ebeit, and W. Hallwachs.

)

ON ELECTEOMAGNETIC EFFECTS PKODUCED BY
ELECTRICAL DISTURBANCES IN INSULATORS

{Siizungaber. d, Berl. Akadem, Nov. 10, 1887. Wiedemann*s Ann. 34,

p. 273.)

It is obviously a fundamental assumption in the most promising
electrical theories that electrical disturbances in insulators are
accompanied, not only by the electrostatic actions (which are
known with certainty to exist), but also by the corresponding
electromagnetic actions. All that we know about electrical
phenomena has long tended to raise this assumption to a high
degree of probability; but as yet it can scarcely be said to follow
with certainty from any direct observations. In the following
pages are described a series of researches which will, I hope,
assist in filling this gap. They exhibit an electromagnetic effect
which proceeds from insulators ; they can be repeated with un-
failing success and without extensive appliances. A magnetic |
effect arising out of processes in an insulator has already been]
exhibited in an experiment by Herr Eontgen,^ if we assume
that the final communication relating to this experiment con-
firms the interpretation first assigned to it.

In order to detect the electromagnetic action, I made use of
the extremely rapid electric oscillations which can be excited in
unclosed metallic conductors by the appropriate use of sparks.^
The method is the following : — A primary conductor in which
oscillations of the kind referred to are excited, acts inductively

^ W. C. Rontgen, Sitzungsber. d. Berl. Acad,, 1885, p. 195. Cp. also the
more recent paper, Sitzungsber, der Berl, Acad., 1888, p. 23.
2 See II. and V.

96 ELECTROMAGNETIC EFFECTS PRODUCED BY vi

upon a secondary conductor. The induced disturbance is
observed by inserting a spark-gap. In order to make the
observation delicate both conductors are adjusted to the same
period of oscillation. The secondary conductor is now brought
as near to the primary as possible, but in such a position that
the forces acting upon its various parts neutralise each other,
SO' that it remains free from sparks. If the equilibrium is
now upset by bringing other conductors near, sparking com-
mences again ; the system acts as a kind of induction-balance.
But it is an induction -balance which has this peculiarity, that
it also indicates a change when large insulating masses are
brought near it. For the oscillations are so rapid that the
quantities of electricity displaced in insulators by dielectric
polarisation are of the same order of magnitude as those which
are set in motion by conduction in metals.

The Apparatus

Fig. 24 shows the apparatus by means of which this
principle was put into practice. Only the essential parts are
shown ; we have to imagine them as connected by a light wooden
frame. AA'\b the primary conductor, consisting of two square
brass plates 40 cm. in the side, which are connected by a
copper wire Y2 c^- thick and 70 cm. long. In the middle of
the latter a spark-gap ^4 cm. is inserted ; the poles consist of
well-polished brass knobs. If we now conduct to the latter the
most powerful discharges of a large induction-coil, the plates
A and A' are first electrified in opposite senses and then, at
the instant when the spark passes, discharge into one another,
thereby giving rise to the oscillations which are peculiar to
the conductor A A', having a period which may be estimated
as the hundred-miUionth part of a second. The discharge of
the induction-coil which immediately follows has no more
effect upon the phenomena which we are here considering than
has the presence of the induction -apparatus and the wires
leading to it. The secondary conductor B forms an exact circle
of 35 cm. radius, and is made of copper wire 2 mm. thick;
it contains at / a spark-gap the length of which can be varied
by a fine screw from a few millimetres down to a few hun-
dredths of a millimetre. A circle having the above dimensions

ELECTRICAL DISTURBANCES IN INSULATORS

Fig. 24.

is in resonance with the primary conductor, and when it is
placed in a suitable position secondary sparks 6-7 mm. long
can be obtained. For the purpose of our experiment the
circle is mounted so
that it can rotate
about an axis passing
through its centre and
perpendicular to its
plane; when the circle
is rotated thus its
position is not altered,
but the spark - gap
rotates with it. The
position of the axis is
such that its direction
lies in the plane of the
plates A and -4', and
in fact coincides with
the line m n which is
symmetrical with re-
spect to them. If we
add that the smallest
distance between A A! and j? is 12 cm., the description of our
apparatus is complete. The phenomena which we now observe
by means of it are the following : —

When the spark-gap/ lies in the horizontal plane of A A\
i.e, at a or at a', it is entirely free from sparks. When the circle
is rotated a few degrees in either direction from this position,
minute sparks arise. These small sparks increase in length
and strength as the spark-gap is removed farther from the
position of equilibrium and reach a maximum length of about
3 mm. when / is at the highest and lowest points, h and V
respectively, of the circle. The oscillations of the secondary
conductor which are thus made manifest are always due to
the forces acting upon those parts of the circle B which are
opposite to the spark-gap. Although in form it is nearly closed,
B must be regardefl as an unclosed circuit ; those parts of it
which lie on either side of the spark-gap act only as capacities
of the ends of the current. The effective force is the resultant
of the electrostatic force and the electromagnetic force which

TJKIVERSITT

98 ELECTROMAGNETIC EFFECTS PRODUCED BY vi

is opposed to it ; the former, being the greater of the two,
determines the direction of the total force. If we regard the
direction of this force and the amplitude of the oscillation
excited by it as being positive when / is at the highest point
of the circle, then we must regard the force and the amplitude
as being negative, with reference to a fixed direction in the
circle B, when / is at the lowest point. The amplitude changes
sign as it passes through zero in the position of equilibriuuL

It will assist us in what follows if we also consider here
the phenomena which occur when we shift the circle B a little
downwards, parallel to itself and without moving it out of its
plane. When this is done the sparking distance iilcreases at
the highest point and diminishes at the lowest point ; the points
which are free from sparks — the null-points as we may call
them — no longer lie on the horizontal line through the axis,
but appear to be rotated downwards through a certain angle
on either side. The slight displacement has changed the
effect of the force of induction, although it has scarcely changed
the effect of the electrostatic force, for the former, when inte-
grated around the closed circle B, now gives an integral which
is not zero ; hence it gives rise to an oscillation the sign of
whose amplitude is independent of the position of the spark-
gap; and according to our convention this sign is positive.
For the direction of the integrated force of induction is oppo-
site to that of the electrostatic force in the upper half, but is
the same as that of the electrostatic force in the lower half of
the circle By in which latter we regard the sign of the electro-
static force as being positive. Since the oscillation which is
now superposed does not differ in phase from -the former one,
their amplitudes are simply added together. This explains
the results observed.

The explanations of the phenomena which we have here
given will be found more completely established in the preced-
ing paper.^

Effects produced hy Approach of Conductors

Hitherto it has been assumed that the conductors A A'
and B are set up in a large room as far away as possible from
all objects which might disturb the action. Such an arrange-

1 See V.

VI ELECTRICAL DISTURBANCES IN INSULATORS 99

ment is necessary if we wish to secure an actual disappearance
of the sparks at a and a\ For we soon observe that sparks
are produced when conductors are brought near, e,g, when
long metal rods are placed on the floor underneath the
apparatus. A little attention shows that even the body of the
observer exerts a perceptible influence. If he places himself
1-2 metres away on the prolongation of the axis mn the
apparatus is free from sparks ; but if he approaches nearer in
order to examine the sparks, he always finds them present.
These very minute sparks have to be observed from a distance,
and it follows as a necessary consequence that the observer
must work in a dark room, and that his eyes must be rendered
more sensitive by not exposing them to light beforehand.

We have now to choose a conductor which will produce
a moderately large effect, and of which we may assume the
oscillation period to be smaller than that of our primary
oscillation. These conditions are fulfilled by the conductor
made of sheet-metal, wliich is shown at C in our illustration.
When it is lowered towards the primary conductor A A\ we
observe the following effects : — The spark-length has decreased
at the highest point &, and has increased at the lowest point V ;
the null-points have moved upwards, Le, towards the conductor
(7, whereas there now is noticeable sparking where the null-points
originally were. From the last experiment in the preceding
section we know what effect would be produced by shifting the
conductor A A' upwards. The same effect — qualitatively — would
be produced by introducing above -4 -4' a second current having
the same direction as that in A A', Now our conductor C
exerts exactly the opposite effect ; and, if we assume that
there exists in (7 a current which is always in the opposite
direction to that in A A\ this effect is naturally explained
as being due to an inductive action proceeding from C. This
assumption is indeed necessary, for the preponderating
electrostatic force tends to produce such a current; and,
since the natural period of oscillation of the conductor is less
than that of the force, the current must have the same phase
as the exciting force. In order to test the correctness of this
explanation I proceeded to experiment further in the following
way: — I left the horizontal plates of the conductor in
position, but removed the vertical sheet, and in place of it

100 ELECTROMAGNETIC EFFECTS PEODUCED BY VI

introduced in succession longer and thinner wires, with a view
to increasing gradually the period of oscillation of the con-
ductor C, The results of this progressive change were as
follows: — ^^At first the null -points retreated farther and
farther upwards, but at the same time became more and
more indistinct ; they were no longer points of extinction, but
simply points of minimum spark-length. Hitherto the spark-
length at the highest point was much smaller than at the
lowest point ; but after the disappearance of the zero-points
it began to increase again. At a certain stage the sparks in
the highest and lowest positions again became equal, but no
null-points could be found anywhere in the circle; in all
positions there was vigorous sparking. From here on the
spark-length at the lowest point grew less, and in its neigh-
bourhood there presently appeared two null-points, which at
first were only feebly marked; these soon became more
distinct, and approached towards the points a and a', but
always lay on the half of the circle remote from the conductor
C, Finally they coincided with the points a and a'; the
electrical condition was now identical with that which
obtained before the conductor G had been brought near.
The successive changes are just what might be expected
according to our conception of the mode of action. For
if the period of oscillation of the conductor C approaches
that of the conductor AA\ the current in C becomes
stronger, but at the same time there arises a difference
of phase between the current and the inducing force.
At the stage where resonance occurs the current in C is
strongest, and the difference of phase amounts (as in every
case of resonance of a moderately damped oscillation) to a
quarter-period; hence there can no longer be any interfer-
ence between the oscillations induced in B hy AA' and
by C respectively. This condition evidently corresponds to
the stage specially referred to above. If the period of
oscillation of C becomes much greater than that of AA^
the amplitude of the oscillations in C again decreases, and
the difference of phase between them and the exciting
force now approaches a half- period. The current in C is
now at every instant in the same direction as that in
AA'\ interference between the oscillations excited in ^ by

VI ELECTRICAL DISTURBANCES IN INSULATORS 101

these currents is again possible; but the effect produced
by the conductor C must be opposite to that which it exerted
in its original position.

If the conductor C is brought very close to ^ ^' only small
sparks appear in the circle B. By bringing the conductors closer
together the period of oscillation of A A' is increased, and thus
A A' and B are no longer in resonance.

Effects produced hy Approach of Non-conductors

A very rough estimate shows that if large masses of in-
sulating substances are brought near to the apparatus, the
quantities of electricity displaced by dielectric polarisation
must be at least as great as those which are set in motion
by conduction in thin metallic rods. The approach of the
latter has been found to produce a very noticeable effect in
our apparatus ; if, therefore, the approach of large insulating
masses produced no simUax effect, we should naturaUy con-
elude that the electricity displaced by dielectric polarisation
did not exert a corresponding electromagnetic action. But if
the views of Faraday and Maxwell are correct, we should
expect that a noticeable effect would be producied, and, further,
that the approach of a non-conductor would act in the same
way as that of a conductor having a very short period of oscilla-
tion. Experiment fully confirms this expectation; and the
only difficulty in carrying out the experiments is that of pro-
curing sufficiently large masses of the insulating material.

I made the first experiments with a material which lay
ready to hand, namely, paper. Underneath the conductor
AA' 1 piled up books in the form of a parallelepiped
1*5 metre long, 0*5 m. broad, and 1 m. high, until they reached
the plates A and A\ It was shown without doubt that
sparks now appeared in those positions of the circle which
before were free from sparks, and that in order to make the
sparks disappear the spark-gap / had to be turned about 10°
towards the pile of books. Encouraged by this, I had
800 kgm. of immixed asphalt cast in the form of a
block 1*4 metre long, 0*6 m. high, and 0*4 m. broad
{D in Fig. 24). The apparatus was removed on to this,
the plates being laid upon the block. The effect could

102 ELECTROMAGNETIC EFFECTS PRODUCED BY vi

be immediately recognised; the results obtaiaed were as
follows : —

1. The spark at the highest point of the circle was now
considerably stronger than at the lowest point (that nearest
the asphalt).

2. The null-points were displaced downwards, i.e, towards
the insulator, and when the plates were laid right upon it
the angle of displacement (which could be measured with
fair accuracy) was 23°. But the sparking no longer ceased
completely at these points. At the original zero-points there
was now vigorous sparking.

3. When the plates A and A^ rested upon the asphalt
block the period of oscillation of A A' was altered ; the period
of oscillation of £ had to be increased at the same time in
order to obtain sparks of maximum length.

4. If the apparatus was gradually removed in any direc-
tion away from the asphalt block the effect continuously
diminished, without experiencing any qualitative change.

We have here all the effects of a conductor of small
period of oscfllation. The accordance between the mode of
action of the insulator and of a conductor is further shown
by the fact that the one can be compensated by the opposing
action of the other. Thus, if the apparatus lay upon the
asphalt, and the conductor C was brought near it from above,
the null -points shifted backwards towards their original
positions, and they again coincided with the points a and
a' when the conductor Cf was brought within about 11 cm.
of the conductor A A!, If the upper surface of the asphalt
lay 5 cm. beneath the plates A and A', compensation was
attained as soon as G was brought within 17 cm. of A A'.
The compensating action always took place when the con-
ductor was somewhat farther off than the insulator. In a
rough way these experiments show that the action of the
insulator is, quantitatively as well as qualitatively, about what
we should expect.

The asphalt used was an excellent insulator; it contained (as
might be suspected from its high specific gravity) a large amount
of mineral matter. One hundred parts (by weight) were found
to give no less than 62 parts of ash, consisting of 17 parts of
quartz-sand, 40 of calcium compounds, and 5 of aluminium and

VI ELECTRICAL DISTURBANCES IN INSULATORS 103

iron compounds.^ It might be suspected that the action should
be attributed entirely to these constituents, some of which
might perhaps act as conductors. In order to remove this doubt
I had a second, and exactly similar, block made of the so-called
artificial pitch : this also is an excellent insulator, and gives
scarcely any ash. The phenomena observed with this were the
same as those above described, excepting that they were not quite
so strongly marked ; for example, the maximum displacement
of the null-points here was only 19°. Unfortunately, however,
this artificial pitch contains not only hydrocarbons but also
free carbon in a very fine state of division, and it would be
difficult to determine the amount of this latter. It cannot be
denied that this carbon would have some conductivity, and
hence the doubt in question is not entirely removed by this
experiment. The expense of undertaking further investiga-
tions on the same large scale with pure substances was pro-
hibitory. I therefore had the system of conductors A A' and
B made again of exactly one-half the linear dimensions, and
tried whether the phenomena could be followed with sufficient
accuracy in this smaller model. The result was satisfactory,
although, of course, with such exceedingly delicate sparks the
strain upon the observer's attention was necessarily increased.
For the purpose of demonstrating the phenomenon, or for
quantitative experiments, it would be advisable to adhere to
the larger dimensions. With the small apparatus I investi-
gated altogether eight substances, which I will now mention
in order : —

1. Asphalt — The large block already described was used.
When the plates A and A' lay upon the block, so that their
front edges lay along the front edge of the block, the rotation
of the null-point amounted to 31°. When the apparatus was
drawn forward, so that the central line r s coincided with the
front edge of the block, the rotation amounted to 20°.

2. Artificicd Pitch obtained from Coal, — Here, again, the
large block was used. The rotations in the two positions
referred to in (1) amounted to 21° and 13° respectively.

3. Paper, — When the apparatus was placed upon a block
of paper 70 cm. long, 35 cm. high, and 20 cm. broad, the
null-points were displaced about 8° towards the paper.

^ For the analysis I have to thank my colleague, Herr Hofrath Engler.

104 ELECTROMAGNETIC EFFECTS PRODUCED BY vi

4. With a block of dense and perfectly dry wood the rota-
tion of the null-points amounted to about 10°.

5. Sandstone, — When the apparatus was brought near to
a sandstone pillar in the building (almost touching it)^ the
null-points were rotated about 20° towards the sandstone. I
had already observed with the large apparatus that the stone
floor exercised a perceptible effect as soon as the apparatus
was brought within half a metre of it.

6. Sulphur. — ^A massive block 70 cm. long, 20 cm.
broad, and 35 cm. high, was cast from roll sulphur in a
wooden mould, and the mould was then removed. The action
of the block was very distinct ; the various effects described
above could be perceived, and the rotation amounted to
13-14°.

7. Paraffin. — The paraffin was white; it melted between
60° and 70°, giving a liquid as clear as water and free from
impurities. It was melted and poured into a cardboard mould
of the same dimensions, which was afterwards removed. The
action was very distinct, and the rotation amounted to 7°.

8. PetroUxim. — In order to investigate the effect of a
liquid insulator, I filled an oak trough with 45 litres of pure
petroleum. The internal dimensions of the trough were : —
Length 70 cm., breadth 20 cm., depth 35 cm. When full it
produced a rotation of about 7°, when empty about 2°. The
very perceptible difference indicates the effect which would be
produced by the petroleum alone.

The concordance between the observations made upon so
many substances, some of which were pure, scarcely leaves
any doubt that the action is a real one, and that it must be
attributed to the substances themselves, and not to impurities
in them. Indeed, I see only two objections which can be
urged against this interpretation of the phenomena, and it will
be advisable to rebut these at once. In the first place, it
might be asserted that the effect is not an electromagnetic one,
but that the insulator changes the distribution of the electro-
static force in its neighbourhood, and that this change in the
distribution results in a change in the phenomenon. I have
tried in vain to interpret, in accordance with this assumption,
the various phenomena observed. But the assertion can be
directly disproved. For, if the insulator fills a space which is

VI ELECTRICAL DISTURBANCES IN INSULATORS 105

only bounded by lines of force, and by parts of the surfaces
of A and A', it cannot give rise to any change in the
electrostatic force outside its own mass. Now the vertical
plane through the centre line r s is certainly made up of
lines of force, and so also is the horizontal plane of the
plates A and A' themselves. If, therefore, the insulator is
bounded by these two planes, and if it extends behind the
former and under the latter, as far as it can exert any influ-
ence, then every electrostatic effect outside the insulator is
avoided. Now if we place our smaller apparatus with the line
r s upon the upper front edge of one of the large blocks, the
conditions referred to are sufficiently fulfilled. , But when this
was done the action, as already stated, did not cease, but was
of similar strength to that observed imder the most favourable
conditions. It follows that the action did not arise from
electrostatic forces.

In the second place, it may be objected that the effects
should be attributed to currents arising through a residual
conductivity. This objection can scarcely be urged with
respect to such excellent insulators as sulphur and paraffin ;
nor do I believe that it is valid in the case of inferior insulators
such as wood. Even assuming that such a substance insulates
so badly that it allows the charged plate A to discharge in the
ten-thousandth part of a second, but not much more rapidly,
then during an oscUlation of our apparatus the plate would
never lose more than the ten-thousandth part of its charge.
The conduction-current proper in the substance under con-
sideration would therefore never exceed the ten-thousandth
part of the primary current in AA\ and hence it would be
quite ineffective. Hence in the case of the better insulators,
at any rate, any assistance through conduction is excluded.

At present it does not appear to be possible to give any
discussion of the quantitative relations of the experiments that
would be of interest.

We have now seen what effect is produced upon the
secondary circuit B by bringing a metallic conductor near
to the primary conductor A A\ If C was in resonance with

106 ELECTROMAGNETIC EFFECTS IN INSULATOBS vi

A A', its action upon B could not interfere with the direct
action of A A', But at the same time, when the conditions
for resonance were fulfilled, its action was fairly powerful, and
could even be perceived when C was removed 1-1*5 metre
away from AA\ Upon this I based experiments which
should establish a finite rate of propagation of the electric
forces. For if these forces require time to proceed in the first
place from AA'Xx^C, and then again from C back to B, the
difference of phase between the effects of A A! upon B and of
C upon B will increase when the distance between A A' and
C increases ; and the two effects must again become capable
of producing interference if the distance between A A! and C
becomes so great that the time taken by the electric force in
traversing it is one-quarter of the half- period of oscillation.
Hitherto these experiments have been unsuccessful, for I have
not been able to detect any of the phenomena which I had
expected. But since it was at best a question of observing
exceedingly delicate changes, I do not consider that this nega-
tive result should weigh against the positive results which I
have obtained otherwise.

VII

ON THE FINITE VELOCITY OF PROPAGATION OF

ELECTROMAGNETIC ACTIONS

{Sitzungshr, d, Berl. Akad, d, Wiss, Feb. 2, 1888. Wiedemann* s Ann,

34, p. 651.)

When variable electric forces act within insulators whose
dielectric constants dififer appreciably from unity, the polarisa-
tions which correspond to these forces exert electromagnetic
eflfects. But it is quite another question whether variable
electric forces in air are also accompanied by polarisations
capable of exerting electromagnetic efifects. We may conclude
that, if this question is to be answered in the afl&rmative,
electromagnetic actions must be propagated with a finite
velocity.

While I was vainly casting about for experiments which
would give a direct answer to the question raised, it occurred
to me that it might be possible to test the conclusion,
even if the velocity under consideration was considerably
greater than that of light. The investigation was arranged
according to the following plan : — In the first place, regular
progressive waves were to be produced in a straight, stretched
wire by means of corresponding rapid oscillations of a primary
conductor. Next, a secondary conductor was to be exposed
simultaneously to the influence of the waves propagated
through the wire and to the direct action of the primary
conductor propagated through the air ; and thus both actions
were to be made to interfere. Finally, such interferences
were to be produced at different distances from the primary
circuit, so as to find out whether the oscillations of the electric

108

FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS

VII

force at great distances would or would not exhibit a retarda-
tion of phase, as compared with the oscillations in the neigh-
bourhood of the primary circuit. This plan has proved to be
in all respects practicable. The experiments carried out in
accordance with it have shown that the inductive action is
undoubtedly propagated with a finite velocity. This velocity
is greater than the velocity of propagation of electric waves in
wires. According to the experiments made up to the present
time, the ratio of these velocities is about 45 : 28. From this
it follows that the absolute value of the first of these is of the
same order as the velocity of light. Nothing can as yet be
decided as to the propagation of electrostatic actions.

The Primary and Secondary Conductors

The primary conductor A A' (Fig. 25) consisted of two
square brass plates, 40 cm. in the side, which were connected

< crz

\2^

Fig. 25.

by a copper wire 60 cm. long. In the middle of the wire was
a spark-gap in which oscillations were produced by very
powerful discharges of an induction-coil J! The conductor
was set up 1*5 metre above the floor, with the wire horizontal
and the plane of the plates vertical. We shall denote as the
base-line of our experiments a horizontal straight line rs
passing through the spark-gap and perpendicular to the direc-
tion of the primary oscillation. We shall denote as the zero-
point a point on this base-line 45 cm. from the spark-gap.

The experiments were carried out in a large lecture-room,
in which there were no fixtures for a distance of 12 metres in

VII FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS 109

the neighbourhood of the base-line.^ During the experiments
this room was darkened.

The secondary circuit used was sometimes a wire C in the
form of a circle of 35 cm, radius, sometimes a wire B bent
into a square of 60 cm. in the side. The spark-gap of both
these conductors .was adjustable by means of a micrometer-
screw ; and in the case of the square conductor the spark-gap
was provided with a lens. Both conductors were in resonance
with the primary conductor. As calculated from the capacity
and coefficient of self-induction of the primary, the (half)
period of oscillation of all three conductors amounted to 1*4
hundred-miUionths of a second.^ Still it is doubtful whether
the ordinary theory of electric oscillations gives correct results
here. But inasmuch as it gives correct values in the case of
Leyden jar discharges, we are justified in assuming that its
results in the present case will, at any rate, be correct as far as
the order of magnitude is concerned.

Let us now consider the influence of the primary oscilla-
tion upon the secondary circuit in some of the positions which
are of importance in our present investigation. First let us
place the secondary conductor with its centre on the base-line
and its plane in the vertical plane through the base-line. We
shall call this the first position. In this position no sparks
are perceived in the secondary circuit. The reason is obvious :
the electric force is at all points perpendicular to the direction
of the secondary wire.

Now, leaving the centre of the secondary conductor still
on the base-line, let it be turned so that its plane is perpen-
dicular to the base-lin^ we shall call this the second position.
Sparks now appear in the secondary circuit whenever the
spark-gap lies above or below the horizontal plane through the
base-line ; but no sparks appear when the spark-gap lies in
this plane. As the distance from the primary oscillator
increases, the length of the sparks diminishes, at first rapidly
but afterwards very slowly. I was able to observe the sparks
along the whole distance (12 metres) at my disposal, and
have no doubt that in larger rooms this distance could be still
farther, extended. In this position the sparks owe their origin

1 [See Note 12 at end of book.] '
^ See II., p. 50. [See also Note IS at end of book.]

110 FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS vii

mainly to the electric force which always acts in the part of
the secondary circuit opposite to the spark-gap. The total
force may be split up into the electrostatic part and the
electromagnetic part ; there is no doubt that at short distances
the former, at greater distances the latter, preponderates and
settles the direction of the total force.

Finally, let the plane of the secondary conductor be
brought into the horizontal position, its centre being still on
the base-line. We shall call this the third position. If we
use the circular conductor, place it with its centre at the zero-
point of the base-line, and turn it so that the spark-gap
slowly moves around it, we observe the following effects : —
In all positions of the spark-gap there is vigorous sparking.
The sparks are most powerful and about 6 mm. long when
the spark-gap faces the primary conductor; they steadily
diminish when the spark-gap is moved away from this posi-
tion, and attain a minimum value of about 3 mm. on the
side farthest from the primary conductor. If the conductor
was exposed only to the electrostatic force, we should expect
sparking when the spark-gap was on the one side or the other
in the neighbourhood of the base-line, but no sparking in the
two intermediate positions. Indeed, the direction of the
oscillation would be determined by the direction of the force
in the portion of the secondary conductor lying opposite
to the spark-gap. But upon the oscillation excited by the
electrostatic force is superposed the oscillation excited by the
electromagnetic force ; and here the latter is very powerful,
because the electromagnetic force when integrated around the
secondary circuit (considered as being closed) gives a finite
integral value. The direction of this integrated force of induc-
tion is independent of the position of the spark-gap; it
opposes the electrostatic force in the part of the secondary
conductor which faces AA^ but reinforces the electrostatic
force in the part which faces away from A A\ Hence the
electrostatic and electromagnetic forces assist each other when
the spark-gap is turned towards, but they oppose each other
when it is turned away from the primary conductor. That it
is the electromagnetic force which preponderates in the latter
position and determines the direction of the oscillation, may
be recognised from the fact that the change from the one state

VII FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS 111

to the other takes place in any position without any extinction
of the sparks. For our purpose it is important to make the
following observations : — If the spark-gap is rotated to the
right or left through 90° from the base-line, it lies at a
nodal point with respect to the electrostatic force, and the
sparks which appear in it owe their origin entirely to the
electromagnetic force, and especially to the fact that the latter,
around the closed circuit, is not zero. Hence, in this particu-
lar position, we can investigate the electromagnetic effect, even
in the neighbourhood of the primary conductor, independently
of the electrostatic effect. V

A complete demonstration of the above explanations will
be found in an earlier paper.^ Some further evidence in
support of these explanations, and of the results arrived at in
my earlier paper, will be found in what follows.

The Waves in the Straight Wire

In order to excite in a wire with the aid of our primary
oscillations waves suitable for our purpose, we proceed as
follows : — Behind the plate A we place a plate P of the same
size. From the latter we carry a copper wire 1 mm. thick to
the point m on the base-line ; from there, in a curve 1
metre long, to the point n, which lies 30 cm. above the spark-
gap, and thence in a straight line parallel to the base-line for
a distance sufficiently great to prevent any fear of disturbance
through reflected waves. In my experiments the wire passed
through the window, then went about 60 metres freely through
the air, and ended in an earth-connection. Special experi-
ments showed that this distance was sufficiently great. If now
we bring near to this wire a metallic conductor in the form
of a nearly closed circle, we find that the discharges of the
induction-coil are accompanied by play of small sparks in the
circle. The intensity of the sparks can be altered by altering
the distance between the plates P and A, That the waves in
the wire have the same periodic time as the primary oscilla-
tions, can be shown by bringing near to the wire one of our
tuned secondary conductors ; for in these the sparks become
more powerful than in any other metallic circuits, whether

1 See v., p. 80.

112 FINITE VELOCITY OF ELECTBOMA.GNETIC ACTIONS vii

larger or smaller. That the waves are regular, in respect to
space as well as time, can be shown by the formation of sta*
tionary waves. In order to produce these, we allow the wire
to end freely at some distance from its origin, and bring near
to it our secondary conductor in such a position that its plane
includes the wire, and that the spark-gap is turned towards
the wire. We then observe that at the free end of the wire
the sparks in the secondary conductor are very small ; they
increase in length as we move towards the origin of the wire ;
at a certain distance, however, they again decrease and sink
nearly to zero, after which they again become longer. We
have thus found a nodal point. If we now measure the wave-
length so found, make the whole length of the wire (reckoned
from the point n) equal to a complete multiple of this length,
and repeat the experiment, we find that the whole length is
now divided up by nodal points into separate waves.^ If we
fix each nodal point separately with all possible care, and
indicate its position by means of a paper rider, we see that
the distances of these are approximately equal, and that the
experiments admit of a fair degree of accuracy. -^

The nodes can also be distinguished from the antinodes in
other ways. If we bring the secondary conductor near to the
wire, in such a position that the plane of the former is per-
pendicular to the latter, and that the spark-gap is neither
turned quite towards the wire nor quite away from it, but is
in an intermediate position, then our secondary circle is in a
suitable position for indicating the existence of forces which
are perpendicular to the direction of the wire. Now, when
the circle is in such a position, we see that sparks appear at
the nodal points, but disappear at the antinodes. If we draw
sparks from the wire by means of an insulated conductor, we
find that these are somewhat stronger at the nodes than at the
antinodes ; but the difference is slight, and for the most part
can only be perceived when we already know where the nodes
and antinodes respectively are situated. The reason why this
latter method and other similar ones give no definite result
is that the particular waves under consideration have other
irregular disturbances superposed upon them. With the aid of
our tuned circle, however, we can pick out the disturbances in

^ [See Note 14 at end of book.]

-I

VII FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS 113

which we are interested, just as particular notes can be picked
out of confused noises by means of resonators.

If we cut through the wire at a node, the phenomena
along the part between it and the origin are not affected : the
waves are even propagated along the part which has been cut
off if it is left in its original position, although their strength
is diminished.

The fact that the waves can be measured admits of
numerous applications. If we replace the copper wire hitherto
used by a thicker or thinner copper wire, or by a wire of
another metal, the nodal points are found to remain in the
same positions. Thus the rate of propagation in all such
wires is the same, and we are justified in speaking of it as a
definite velocity. Even iron wires are no exception to this
general rule ; hence the magnetic properties of iron are not
called into play by such rapid disturbances. It will be of
interest to test the behaviour of electrolytes. The fact that
the dectrical disturbance in these is bound up with the dis-
turbance of inert matter might lead us to expect a smaller
velocity of propagation.^ Through a tube of 10 mm. diameter,
filled with a solution of copper sulphate, the waves would not
travel at all ; but this may have been due to the resistance
being too great. Again, by measuring the wave-lengths, we
can determine the relative periods of oscillation of different
primary conductors ; it should be possible to compare in this
way the periods of oscillation of plates, spheres, ellipsoids,
etc.

• In our particular case the nodal points proved to be very
distinct when the wire was cut off at a distance of either
8 metres or 5*5 metres from the zero-point of the base-line.
In the former case the positions of the paper riders used for
fixing the nodal points were — 0*2 m., 2*3 m., 5*1 m., and 8 m. ;
in the latter case — 01 m., 2*8 m., and 5*5 m., the distances
being measured from the zero-point. From this it appears
that the (half) wave-length in the free wire cannot differ much
from 2*8 metres. We can scarcely be surprised at finding
that the first wave-length, reckoned from P, appears smaller
than the rest, when we take into consideration the presence of
the plate and the bending of the wire. A period of oscilla-

^ [See Note 15 at end of book.]
I

lU FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS vii

tion of 1*4 hundred-millionths of a second, and a wave-length
of 2*8 metres, gives 200,000 kin./sec. as the velocity of
electric waves in wires.^ In the year 1850 Fizeau and
Gounelle,^ making use of a very good method, found for this
velocity the value 100,000 km./sec. in iron wires, and
180,000 km./sec. in copper wires. In 1875 W. Siemens,^
using discharges from Leyden jars, found velocities from
200,000 to 260,000 km./sec. in iron wires. Other determin-
ations can scarcely be taken into consideration. Our result
comes in well between the above experimental values. Since
it was obtained with the aid of a doubtful theory, we are not
justified in publishing it as a new measurement of this same
velocity ; but, on the other hand, we may conclude, from the
accordance between the experimental results, that our calcu-
lated value of the period of oscillation is of the right order of
magnitude.

Interference between the direct Action and that propagated

through the Wire

Let us place the square circuit B at the zero-point in
our second position, and so that the spark-gap is at the
highest point. The waves in the wire now exert no influence ;
the direct action gives rise to sparks 2 mm. long. If we now
bring B into the first position by turning it about a vertical
axis, it is found conversely that the primary oscillation exercises
no direct effect ; but the waves in the wire now induce sparks
which can be made as long as 2 mm. by bringing P near to
A. In intermediate positions both causes give rise to sparks,
and it is thus possible for them, according to their diiBFerence in
phase, either to reinforce or to weaken each other. Such a
phenomenon, in fact, we observe. For, if we adjust the plane
of B so that its normal towards A A' points away from that
side of the primary conductor on which the plate P is placed,
the sparking is even stronger than it is in the principal
positions ; but if we adjust the plane of B so that its normal
points towards P, the sparks disappear, and only reappear

^ [See Note 16 at end of book.]

2 Fizeau and Gounelle, Pogg. Ann. 80, p. 158, 1850.

3 W. Siemens, Pogg. Ann, 157, p. 309, 1876.

VII FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS 115

when the spark-gap has been considerably shortened. If,
under the same conditions, we place the spark-gap at the
lowest point of By the disappearance of the sparks takes place
when the normal points away from P. Further modifications
of the experiment — e.g, by carrying the wire beneath the
secondary conductor — produce just such effects as might be
expected from what has above been stated. The phenomenon
itself is just what we expected ; let us endeavour to make it
clear that the action takes place in the sense indicated in our
explanation. In order to fix our ideas, let us suppose that
the spark-gap is at the highest point, and the normal turned
towards P (as in the figure). At the particular instant under
consideration let the plate P have its largest positive charge.
The electrostatic force, and therefore the total force, is directed
from A towards A', The oscillation induced in B is deter-
mined by the direction of the force in the lower part of B,
Positive electricity will therefore be urged towards A^ in the
lower part, and away from A' in the upper part. Let us now
consider the action of the waves. As long as .4 is positively
charged, positive electricity flows away from the plate P.
At the instant under consideration this flow reaches its
maximum development in the middle of the first half wave-
length of the wire. At a quarter wave-length farther from
the origin — that is, in the neighbourhood of our zero-point —
it is just beginning to take up this direction (away from the
zero-point). Hence at this point the electromagnetic induction
urges positive electricity in its neighbourhood towards the origin.
In particular, positive electricity in our ponductor B is thrown
into a state of motion in a circle, so that in the upper part it
tends to flow towards A\ and in the lower part away from
A', Thus, in fact, the electrostatic and electromagnetic forces
act against one another, and are in approximately the same
phase ; hence they must more or less annul one another. If
we rotate the secondary circle through 90° (through the first
position) the direct action changes its sign, but the action of
the waves does not ; both causes reinforce one another. The
same holds good If the conductor B is rotated in its own
plane until the spark-gap lies at its lowest point./

We now replace the wire mn hj longer lengths of wire.
We observe that this renders the interference more indistinct ;

116 FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS vii

it disappears completely when a piece of wire 250 cm. long
is introduced ; the sparks are of the same length whether the
normal points away from P or towards it. If we lengthen
the wire still more the diflference of behaviour in the various
quadrants again exhibits itself, and the extinction of the
sparks becomes fairly sharp when 400 cm. of wire is intro-
duced. But there is now this diflference — that extinction
occurs when the spark-gap is at the top, and the normal
points away from P. Further lengthening of the wire causes
the interference to disappear once more ; but it reappears in
the original sense when about 6 metres of wire are introduced.
These phenomena are obviously explained by the retardation
of the waves in the wire, and they also make it certain that
the state of aflfairs in the progressive waves changes sign
about every 2j8 metres.

If we wish to produce interference while the secondary
circle C lies in the third position, we must remove the recti-
linear wire from the position in which it has hitherto remained,
and carry it along in the horizontal plane through (7, either on
the side towards the plate Ay or on the side towards the plate
A'. In practice it is sufificient to stretch the wire loosely,
grasp it with insulating tongs, and bring it alternately near
one side or the other of C. What we observe is as follows : —
If the waves are carried along the side on which the plate P
Ues, they annul the sparks which were previously present ; if
they are carried along the opposite side they strengthen the
sparks which were already present. Both results always
occur, whatever may be the position of the spark-gap in the
circle. We have seen that at the instant when the plate A
has its Strongest positive charge, and when, therefore, the
primary current begins to flow away from A, the surging at
the first nodal point of the rectilinear wire begins to flow
away from the origin of the wire. Hence both currents flow
round C in the same sense when the rectilinear wire lies on
the side of which is remote from A ; in the other case
they flow round C in opposite senses, and their actions annul
one another. The fact that the position of the spark-gap is
of no importance confirms our supposition that the direction
of the oscillation is here determined by the electromagnetic
force. The interferences which have just been described also

VII FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS 117

change their sign when 400 cm. of wire, instead of 100 cm.,
is introduced between the points m and n,

I have also produced interferences in positions in which
the centre of the secondary circle lay outside the base-line ;
but for our present purpose these are only of importance
inasmuch as they throughout confirmed our fundamental
views.

Interference at Various Distances

Interferences can be produced at greater distances in the
same way as at the zero-point In order that they may be
distinct, care must be taken that the action of the waves
in the wire is in all cases of about the same magnitude as the
direct action. This can be secured by increasing the distance
between F and A, Now very little consideration will show
that, if the action is propagated through the air with infinite
velocity, it must interfere with the waves in the wire in
opposite senses at distances of half a wave-length (ix, 2'8 metres)
along the wire. Again, if the action is propagated through
the air with the same velocity as that of the waves in the
wire, the two will interfere in the same way at all distances.
Lastly, if the action is propagated through the air with a
velocity which is finite, but different from that of the
waves in the wire, the nature of the interference will alter-
nate, but at distances which are farther than 2*8 metres
apart.

In order to find out what actually took place, I first made
use of interferences of the kind which were observed in
passing from the first into the second position. The spark-
gap was at the top. At first I limited myself to distances up
to 8 metres from the zero-point. At the end of each half-metre
along this position the secondary conductor was set up and
examined in order to see whether any difference could be
observed at the spark-gap according as the normal pointed
towards P or away from it. If there was no such difference,
the result of the experiment was indicated by the symbol 0.
If the sparks were smaller when the normal pointed towards
P, then this showed an interference which was represented by
the symbol + . The symbol — was used to indicate an inter

118 FINITE VELOCITr OF ELECTROMAGNETIC ACTIONS -sll

ference when the normal pointed towards the other aide. In
order to multiply the experiments I frequently repeated them,
making the wire mn 50 cdl longer each time, and thus
lengthening it gradually from 100 cm, to 600 cm. The
reaalt3 of my experiments are contained in the following
summary which will easily be understood ; —

100

^1 ^

160

200

()

-I-

280

300

350

()

400

()

460

()

500

550

oi -

eoo

According to this it might almost appear as if the inter-
ferences changed sign at every half wave-length of the waves
in the wlre.^ But, in the first place, we notice that this does
not exactly happen. If it did, then the symbol should
recur at the distances 1 m., 3-8 m., 6'6 m., whereas it obviously
recurs less frequently. In the second place, we notice that
the retardation of phase proceeds more rapidly in the neigh-
bourhood of the origin than at a distance from it. All the
rows agree in showing this. An alteration in the rate of
propagation is not probable. We can with much better reason
attribute this phenomenon to the fact that we are making
use of the total force {Oesamviikraft), which can be split up
into the electrostatic force and the electromagnetic. !Now,
according to theory, it is probable that the former, which
preponderates in the neighbourhood of the primary oscillation,
is propt^ated more rapidly than the latter, which is almost
the only factor of importance at a distance. In order first to
settle what actually happens at a greater distance, I have
extended the experiments to a distance of 12 metres, for at any

'■ [See Note 17 St end of book.]

VII

FINITE VELOCITY OF KLECTROMAGNE

119

rate three values of the length mn, I must admit that this
required rather an effort. Here are the results : —

100

' +

—

250

—

400

1
1

—

If we assume that at considerable distances the electromag-
netic action alone is effective, then we should conclude from
these observations that the interference of this action with
the waves in the wires only changes its sign every 7 metres.

In order now to investigate the electromagnetic force in the
neighbourhood of the primary oscillation (where the phenomena
are more distinct) as well, I made use of the interferences
which occur in the third position when the spark-gap is
rotated 90° away from the base-line. The sense of the
interference at the zero-point has already been stated, and this
sense will be indicated by the symbol — , whereas the symbol
+ will be used to denote an interference by conducting the
waves past the side of G which is remote from F. This choice
of the symbols will be in accord with the way in which we
have hitherto used them. For since the electromagnetic force is
opposed to the total force at the zero-point, our first table
would also begin with the symbol — , provided that the in-
fluence of the electrostatic force could have been eliminated.
Now experiment shows, in the first place, that interference still
takes place up to a distance of 3 metres, and that it is of the
same sign as at the zero-point. This experiment, repeated
often and never with an ambiguous result, is suflScient to prove
the finite rate of propagation of the electromagnetic action.
Unfortunately the experiments could not be extended to a
greater distance than 4 metres, on account of the feeble nature
of the sparks. Here, again, I repeated the experiments with
variable lengths of the wire m n, so as to be able to verify the
retardation of phase along this portion of the wire. The
results are' given in the following summary : —

120

FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS

VII

100

mm^

400

160

—

450

200

500

250

550

—

300

600

—

350

A discussion of these results shows that here, again, the
phase of the interference alters as the distance increases, so
that a reversal of sign might be expected at a distance of
7-8 metres.

But this result is much more plainly shown by combining
the results of the second and third summary — using the data
of the latter up to a distance of 4 metres, and of the former for
greater distances. In the first of these intervals we thus
avoid the action of the electrostatic force by reason of the
peculiar position of our secondary conductor; in the second
this action drops out of account, owing to the rapid weakening
of that force. We should expect the observations of both
intervals to fit into one another without any break, and our
expectation is confirmed. We thus obtain by collating the
symbols the following table for the interference of the electro-
magnetic force with the action of the waves in the wire : —

100

m.^

.—

—

260

—

400

—

From this table I draw the following conclusions : —

1. The interference does not change sign every 2*8 metres.
Therefore the electromagnetic actions are not propagated with
infinite velocity.

2. The interference, however, is not in the same phase at
all points. Therefore the electromagnetic actions do not spread
out in air with the same velocity as the electric waves in
wires.

3. A gradual retardation of the waves in the wire has the

VII FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS 121

efifect of shifting any particular phase of the interference
towards the origin of the waves. From the direction of this
shifting it follows that of the two different rates of propaga-
tion that through air is the more rapid. For if by retardation
of one of the two actions we bring about an earlier coincidence
of both, then we must have retarded the slower one.

4. At distances of every 7*5 metres the sign of the interfer-
ence changes from H- to — . Hence, after proceeding every 7*5
metres, the electromagnetic action outruns each time a wave in
the wire. While the former travelled 7*5 metres, the latter
travelled 7*5 — 2*8 = 4-7 metres. The ratio of the two velocities
is therefore as 75 : 47, and the half wave-length of the electro-
magnetic action in air is 2*8 x 75/47 = 4*5 metres. Since this
distance is traversed in 1*4 hundred-millionths of a second, it
follows that the absolute velocity of propagation in air is
320,000 km. per second. This result only holds good as far
as the order of magnitude is concerned ; still the actual value
can scarcely be greater than half as much again, and can
scarcely be less than two-thirds of the value stated. The
actual value can only be determined by experiment when we
are able to determine the velocity of electricity in wires more
accurately than has hitherto been the case.

Since the interferences undoubtedly change sign after
2*8 metres in the neighbourhood of the primary oscillation, we
might conclude that the electrostatic force which here pre-
dominates is propagated with infinite velocity. But this con-
clusion would in the main depend upon a single change of
phase, and this one change can be explained (apart from any
retardation of phase) by the fact that, at some distance from
the primary oscillation, the amplitude of the total force under-
goes a change of sign. If the absolute velocity of the electro-
static force remains for the present unknown, there may yet
be adduced definite reasons for believing that the electrostatic
and electromagnetic forces possess different velocities. The
first reason is that the total force does not vanish at any point
along the base-line. Since the electrostatic force preponderates
at small distances, and the electromagnetic force at greater
distances, they must in some intermediate position be equal
and opposite, and, inasmuch as they do not annul one another,
they must reach this position at different times.

122 FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS vii

The second reason is derived from the propagation of the
force throughout the whole surrounding space. In a previous
paper ^ it has already been shown how the direction of the
force at any point whatever can be determined. The dis-
tribution of the force was there described, and it was remarked
that there were four points in the horizontal plane, about
1*2 metre before and behind the outer edges of our plates A and
A\ at which no definite direction could be assigned to the
force, but that the force here acts with about the same strength
in all directions. The only apparent interpretation of this
is that the electrostatic and electromagnetic components
here meet one another at right angles, and are about equal
in strength but differ notably in phase; thus they do not
combine to produce a resultant rectilinear oscillation, but a
resultant which during each oscillation passes through all
points of the compass.

The fact that diiBFerent components of the total force
possess different velocities is also of importance, inasmuch as
it provides a proof (independent of those previously mentioned)
that at least one of these components must be propagated with
finite velocity.

Conclimons

More or less important improvements in the quantitative
results of this first experiment may result from further experi-
ments in the same direction ; but the path which they must
follow may be said to be already made, and we may now
regard it as having been proved that the inductive action
is propagated with finite velocity. Sundry conclusions follow
from the results thus obtained, and to some of these I wish to
draw attention.

1. The most direct conclusion is the confirmation of
Faraday's view, according to which the electric forces are
polarisations existing independently in space. For in the
phenomena which we have investigated such forces persist in
space even after the causes which have given rise to them
have disappeared. Hence these forces are not simply parts or
attributes of their causes, but they correspond to changed con-

1 See v., p. 80.

VII FINITE VELOCITY OF ELECTROMAGNETIC ACTIONS 123

ditions of space. The mathematical character of these con-
ditions justifies us then in denoting them as polarisations,
whatever the nature of these polarisations may be.

2. It is certainly remarkable that the proof of a finite
rate of propagation should have been first brought forward in
the case of a force which diminishes in inverse proportion to
the distance, and not to the square of the distance. But it is
worth while pointing out that this proof must also affect
such forces as are inversely proportional to the square of the
distance. For we know that the ponderomotive attraction
between currents and their magnetic actions are connected
by the principle of the conservation of energy with their
inductive actions in the strictest way, the relation being
apparently that of action and reaction. If this relation is not
merely a deceptive semblance, it is not easy to understand
how the one action can be propagated with a finite and the
other with an infinite velocity.

3. There are already many reasons for believing that the
transversal waves of light are electromagnetic waves ; a firm
foundation for this hypothesis is furnished by showing the
actual existence in free space of electromagnetic transversal
waves which are propagated with a velocity akin to that of
light. And a method presents itself by which this important
view may finally be confirmed or disproved. For it now
appears to be possible to study experimentally the properties
of electromagnetic transversal waves, and to compare these
with the properties of light waves.

4. The hitherto undecided questions of electromagnetics
which relate to unclosed currents should now be more easily
attacked and solved. Some of these questions, indeed, are
directly settled by the results which have already been
obtained. In so far as electromagnetics only lacks certain
constants, these results might even suflSce to decide between
the various conflicting theories, assuming that at least one of
them is correct.

Nevertheless, I do not at present propose to go into these
applicatiqns, for I wish first to await the outcome of further
experiments which are evidently suggested in great number by
our method.

VIII

ON ELECTROMAGNETIC WAVES IN AIR AND THEIR

REFLECTION

(Wiedemann's Ann. 34, p. 610, 1888.)

I HAVE recently endeavoured to prove by experiment that
electromagnetic actions are propagated through air with finite
velocity.^ The inferences upon which that proof rested appear
to me to be perfectly valid ; but they are deduced in a com-
plicated manner from complicated facts, and perhaps for this
reason will not quite carry conviction to any one who is not
already prepossessed in favour of the views therein adopted.
In this respect the demonstration there given may be fitly
supplemented by a consideration of the phenomena now to
be described, for these exhibit the propagation of induction
through the air by wave-motion in a visible and almost
tangible form. These new phenomena also admit of a direct
measurement of the wave-length in air. The fact that the
wave-lengths thus obtained by direct measurement only differ
slightly from the previous indirect determinations (using the
same apparatus), may be regarded as an indication that the
earlier demonstration was in the main correct.

In experimenting upon the action between a rectilinear
oscillation and a secondary conductor I had often observed
phenomena which seemed to point to a reflection of the
induction action from the walls of the building. For example,
feeble sparks frequently appeared when the secondary con-
ductor was so situated that any direct action was quite
impossible, as was evident from simple geometrical considera-

1 See VII., p. 107.

VIII ELECTROMAGNETIC WAVES IN AIB AND THEIR REFLECTION 125

tions of symmetry ; and this most frequently occurred in the
neighbourhood of solid walls. In especial, I continually
encountered the following phenomenon: — In examining the
sparks in the secondary conductor at great distances from the
primary conductor, when the sparks were already exceedingly
feeble, I observed that in most positions of the secondary
conductor the sparks became appreciably stronger when I
approached a solid wall, but again disappeared almost suddenly
close to the wall. It seemed to me that the simplest way of
explaining this was to assume that the electromagnetic action,
spreading outwards in the form of waves, was reflected from
the walls, and that the reflected waves reinforced the advancing
waves at certain distances, and weakened them at other
distances, stationary waves in air being produced by the
interference of the two systems. As I made the conditions
more and more favourable for reflection the phenomenon
appeared more and more distinct, and the explanation of it
given above more probable. But without dwelling upon these
preliminary trials I proceed at once to describe the principal
experiments.

The physics lecture-room in which these experiments were
carried out is about 15 metres long, 14 metres broad, and 6
metres high. Parallel to the two longer walls there are two
rows of iron pillars, each of which rows behaves much like a
solid wall towards the electromagnetic action, so that the parts
of the room which lie outside these cannot be taken into con-
sideration. Thus only the central space, 15 metres long, 8*5
metres broad, and 6 metres high, remained for the purpose of
experiment. From this space I had the hanging parts of the
gas-pipes and the chandeliers removed, so that it contained
nothing except wooden tables and benches which could not
well be removed. No objectionable effects were to be feared
from these, and none were observed. The front wall of the
room, from which the reflection was to take place, was a mas-
sive sandstone wall in which were two doorways, and a good
many gas-pipes extended into it. In order to give the wall
more of the nature of a conducting surface a sheet of zinc 4
metres high and 2 metres broad was fastened on to it; this
was connected by wires with the gas-pipes and with a neigh-
bouring water-pipe, and especial care was taken that any

126 ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION Vlii

electricity that might accumulate at the upper and lower ends
of the sheet should be able to flow away as freely as possible.

The primary conductor was set up opposite the middle of
this wall at a distance of 13 metres from it, and was there-
fore 2 metres away from the opposite wall. It was the same
conductor that had already been used in the experiments on
the rate of propagation. The direction of the conducting wire
was now vertical; hence the forces which have here to be
considered oscillate up and down in a vertical direction. The
middle point of the primary conductor was 2*5 metres above
the level floor; the observations were also carried" out at the
same distance above the floor, a gangway for the observer
being built up with tables and boards at a suitable height.
We shall denote as the normal a straight line drawn from the
centre of the primary conductor perpendicularly to the reflect-
ing surfaca Our experiments are restricted to the neighbour-
hood of this normal ; experiments at greater angles of incidence
would be complicated by having to take into consideration the
varying polarisation of the waves. Any vertical plane parallel
to the normal will be called a plane of oscillation, and any
plane perpendicular to the normal will be called a wave-
plane.

The secondary conductor was the circle of 35 cm.
radius, which had also been used before. It was mounted so
as to revolve about an axis passing through its centre and
perpendicular to its plane. In the experiments the axis was
horizontal; it was mounted in a wooden frame, so that both
circle and axis could be rotated about a vertical axis. For
the most part it does well enough for the observer to hold the
circle, mounted in an insulating wooden frame, in his hand,
and then to bring it as may be most convenient into the
various positions. But, inasmuch as the body of the observer
always exercises a slight influence, the observations thus
obtained must be controlled by others obtained from greater
distances. The sparks too are strong enough to be seen in
the dark several metres off; but in a well-lit room practically
nothing can be seen, even at close quarters, of the phenomena
which are about to be described.

After we have made these preparations the most striking
phenomenon that we encounter is the following : — We place

VIII ELECTROMAGNEXrC WAVES IN AIR AND THEIR REFLECTION 127

the secondary circle with its centre on the normal and its
plane in the plane of oscillation, and turn the spark-gap first
towards the wall and then away from it. Generally the
sparks differ greatly in the two positions. If the experiment
is arranged at a distance of about 0*8 metre from the wall the
sparks are much stronger when the spark-gap is turned
towards the wall. The length of the sparks can be so regu-
lated that a continuous stream of sparks passes over when the
spark-gap is turned towards the wall, whereas no sparks what-
ever pass over in the opposite position. If we repeat the
experiment at a distance of 3 metres from the wall we find,
on the contrary, a continuous stream of sparks when the
spark-gap is turned away from the wall, whereas the sparks
disappear when the spark-gap is turned towards the wall. If
we proceed further to a distance of 5*5 metres, a fresh reversal
has taken place ; the sparks on the side towards the wall are
stronger than the sparks on the opposite side. Finally, at a
distance of 8 metres from the wall, we find that another
reversal has been executed ; the sparking is stronger on the
side remote from the wall, but the difference is no longer
so noticeable. Nor does any further reversal occur ; for it is
prevented by the preponderating strength of the direct action
and by the complicated forces which exist in the neighbour-
hood of the primary oscillation. Our figure (the scale in
which indicates the distances from the wall) shows at I., II.,
III., IV., the secondary circle in those positions in which the
sparks were most strongly developed. The alternating char-
acter of the conditions of the space is clearly exhibited.

At distances lying between those mentioned both sets of
sparks under consideration were of equal strength, and in the
immediate neighbourhood of the wall too the distinction
between them diminishes. We may therefore denote these
points— namely, the points A, B, C, D in the figure— as being
nodal points in a certain sense. Still we must not consider the
distance between any one of these points and the next as being
the half wave-length. For if all the electrical disturbances
change their direction in passing through one of these points,
then the phenomena in the secondary circle should repeat
themselves without reversal ; for in the spark-length there is
nothing which corresponds to a change of direction in the

128 BLECTBOMAGNETIC WAVES IN AIR AND THEIR REFLECTION viii

oscillation. We should rather conclude from these experi-
ments that in passing through any one of these points one
part of the action undeigoes reversal, while another part does
not. On the other hand, it is allowable to assume that double
the distance between any two of the points corresponds to the
half wave-length, so that these points each indicate the end of
a quarter wave-length. And, indeed, on the basis of this
assumption and of the fundamental view just expressed, we
shall arrive at a complete explanation of the phenomenon'.

For let us suppose that a vertical wave of electric force
proceeds towards the wall, is reflected with slightly diminished
intensity, and so gives rise to stationary waves. If the wall

Pig. 26.

were a perfect conductor a node would form at its very sur-
face. For inside a conductor or at its boundary the electric
force must always be vanishingly small. Now our wall
cannot be regarded as a perfect conductor. For, in the first
place, it is only metallic in part, and the part which is metallic
is not very extensive. Hence at its surface the force will
still have a certain value, and this in the sense of the
advancing wave. The node, which would be formed at the
wall itself if it were perfectly conducting, must therefore lie
really somewhat behind the surface of the wall, say at the
point A in the figure. If double the distance A By that is the
distance A G, corresponds to the half wave-length, then the
geometrical relations of the stationary wave are of the kind

VIII ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION 1 29

which are represented in the usual symbolic fashion by the
continuous wave-line in the figure. The forces acting on both
sides of the circle in the positions /, //, ///, and IV are
correctly represented for any given instant in magnitude and
direction by the arrows at the sides. If, then, in the neigh-
bourhood of a node the. spark-gap is turned towards the node,
we have in the circle a stronger force acting under favourable
conditions against a weaker force, which acts under unfavour-
able conditions. But if the spark-gap is turned away from
the node, the stronger force now acts under unfavourable con-
ditions against a weaker force, which in this case is' acting
under favourable conditions. And whether in this latter
case the one preponderates or the other, the sparks must
necessarily be weaker than in the former case. Thus the
change of sign of our phenomenon every quarter wave-length
is explained.

Our explanation carries with it a means of further testing
its correctness. If it is correct, then the change of sign at
the points B and D should occur in a manner quite different
from the change of sign at C, At V, VI, and VII in the
figure the circle and the acting forces in these positions are
represented, and it is easily seen that if at jB or i> we transfer
the spark-gap from the one position to the other by rotating
the circle within itself, the oscillation changes its direction
relatively to a fixed direction within the circle ; during this
rotation the sparks must therefore become zero either once or
an uneven number of times. On the other hand, if the same
operation is performed at C, the direction of the oscillation
does not change ; and therefore the sparks must either not
disappear at all, or else they must disappear an even number
of times. Now when we actually make the experiment, what
we observe is this : — At B the intensity of the sparks
diminishes as soon as we remove the spark-gap from a,
becomes zero at the highest point, and again increases to its
original value when we come to y8. Similarly at i>. At C,
on the other hand, the sparks persist without change during
the rotation, or, if anything, are somewhat stronger at the
highest and lowest points than at those which we have been
considering. Furthermore, it strikes the observer that the
change of sign ensues after a much smaller displacement at C

130 ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION viii

than at B and D, so that in this respect also there is a
contrast between the change at C and that at B and D.

The representation of the electric wave which we have
thus sketched can be verified in yet another way, and a very
direct one. Instead of placing the plane of our circle in the
plane of oscillation, let us place it in the wave-plane; the
electric force is now equally strong at all parts of the circle,
and for similar positions of the sparks their intensity is simply
proportional to this electric force. As might be expected, the
sparks are now zero at the highest and lowest points of the
circle at all distances, and are strongest at the points along
the normal in a horizontal plane. Let us then bring the
spark-gap into one of these latter positions, and move slowly
away from the walL This is what we observe : — Just at the
conducting metallic surface there are no sparks, but they make
their appearance at a very small distance from it; they
increase rapidly, are comparatively strong at B, and then again
diminish. At G again they are exceedingly feeble, but become
stronger as we proceed further. They do not, however, again
diminish, but continue to increase in strength, because we are
now approaching the primary oscillation. If we were to
illustrate the strength of the sparks along the interval ADhy
a curve carrying positive and negative signs, we should obtain
almost exactly the curve which has been sketched. And
perhaps it would have been better to start from this experi-
ment. But it is not really so striking as the first one de-
scribed ; and furthermore, a periodic change of sign seems to be
a clearer proof of wave-motion than a periodic waxing and
waning.

We are now quite certain that we have recognised nodes
of the electric wave at A and C, and antinodes at B and I).
We might, however, in another sense call B and I) nodes, for
these points are nodes of a stationary wave of magnetic force,
which, according to theory, accompanies the electric wave and
is displaced a quarter wave-length relatively to it. This
statement can be illustrated experimentally as follows : — We
again place our circle in the plane of oscillation, but now
bring the spark-gap to the highest point. In this position
the electric force, if it were homogeneous over the whole
extent of the secondary circle, could induce no sparks. It

VIII ELECTEOMAGNETIC WAVES IN AIR AND THEIR REFLECTION 131

only produces an eftect in so far as its magnitude varies in
various parts of the circle, and its integral taken around the
circle is not zero. This integral is proportional to the number
of lines of magnetic force which flow backwards and forwards
through the circle. In this sense, we may say that in this
position, the sparks measure the magnetic force, which is
perpendicular to the plane of the circle.^ But now we find
that in this position near the wall there is vigorous sparking
which rapidly diminishes, disappears at B, increases again up to
C, then again decreases to a marked minimum at D, after which
it continuously increases as we approach the primary oscilla-
tion. Eepresenting the strength of these sparks as ordinates
with positive and negative signs, we obtain approximately the
dotted line of our figure, which thus represents correctly the
magnetic wave. The phenomenon which we first described
can also be explained as resulting from the co-operation of the
electric and the magnetic force. The former changes sign at
the points A and (7, the latter at the points B and D ; thus
one part of the action changes sign at each of these points
while the other retains its sign; hence the resulting action
(as the product) changes sign at each of the points. Clearly
this explanation only differs in mode of expression, and not
in meaning, from the one first given.

Hitherto we have only considered the phenomena in some
of the more important positions of the circle. The number of
transitions between these is in a threefold sense infinite. We
shall therefore content ourselves with describing the transitions
for the case in which the plane of the circle lies in the plane
of oscillation. Near the wall the sparking is greatest on the
side towards the wall, and least on the opposite side; on
rotating the circle within itself the sparking changes from the
one value to the other, attaining only intermediate values ;
there are no zero-points in the circle. As we move away from
the wall the sparking on the side remote from it gradually
diminishes and becomes zero when the centre of the circle is
1*08 metre distant from the wall; this distance can be
ascertained within a few centimetres. As we proceed further,
the sparks on the side remote from the wall reappear and at
first are still weaker than on the side towards the wall ; but

^ [See Note 18 at end of book.]

132 ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION viii

the strength of the sparks does not change from the one value to
the other simply by passing through intermediate values ; on
rotating the circle within itself the sparking becomes zero once
in the upper and once in the lower half of the circle. The
two zero-points develop out of the one which was first formed
and separate gradually more from each other, until at B they
lie at the highest and lowest points of the circle. By this
indication the point B can be determined with fair accuracy,
but more exactly still by a further observation of the zero-
points. On proceeding further, these zero-points slide over
towards the side of the circle facing the wall, approach each
other, and again coincide in a single zero-point at a certain
distance from the wall which can be sharply determined. In
this case the distance of the centre from the wall is 2*35
metres. The point B must lie exactly between this and the
analogous point first observed, i,e. at a distance of 1*72 metres
from the wall ; this agrees within a few centimetres with the
direct observation. If we proceed further towards C the
sparks at all points of the circle tend to become of equal
strength, and do become so at C, Beyond C the same per-
formance begins over again. In this region there are no zero-
points in the circle. In spite of this the position of the point
G can be determined with fair accuracy, inasmuch as in
its neighbourhood the phenomena first described alter very
rapidly. In my experiments (7 was 4*10 to 4*15 metres, or
say 4' 12 metres from the wall. The point D could not be
accurately determined for the phenomena had here become
very feeble ; only this much could be asserted, that its distance
from the wall was between 6 and 7*5 metres. For an
explanation of the details I may refer to a previous paper.^ .^

The mathematical developments therein indicated admit of
being carried much further ; but the experiments seem to be
suflftciently intelligible without calculation.

According to our measurement, the distance between B
and C is 2*4 metres. If we assume this to be the correct
value, the nodal point A lies 0*68 metres behind the wall, the J

point i> 6'52 metres in front of it, which agrees suflftciently
well with the experiments. According to this, the half wave-
length is 4*8 metres. By an indirect method I had obtained

1 See v., p. 80.

VIII ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION 133

4*5 metres as the wave-length for the same apparatus. The
difference is not so great as to prevent us from regarding the
new measurement as confirming the earlier one.^ If in our
earlier measurements we substitute 2*9 for 2*8 metres as the
wave-length in the wire, and 7*1 for 7*5 as the length of the
coincidence (which will be found to agree with the observa-
tions), we can deduce the new value from the earlier observa-
tions. Perhaps, indeed, a mean value would be nearest to the
truth ; and I scarcely think it likely that the nodal point A
should lie nearly 0*7 metre behind the metallic wall.
Assuming a mean value for the wave-length, and a velocity of
propagation equal to that of light, we get for the period of
oscillation of our apparatus about 1*55 hundred-millionths of a
second, instead of the 1*4 hundred-millionths obtained by
calculation.

I have repeated the experiments with some alterations.
Altering the distance of the primary oscillation from the
reflecting wall did not result in much fresh information. If
this distance could have been considerably extended, we might
certainly have expected a distinct formation of a second and
third wave-length ; but there was not sufficient space for such
extension. When the distance was diminished the phenomena
simply became less interesting, for towards the primary
oscillation they were more and more indistinct, and in the
opposite direction the reversal of sign became lost The
experiments with an oscillation of different period are better
worth describing, for they show that the points which have
attracted our attention are determined, not by the form of the
wall or of the room, but only by the dimensions of the primary
and of the secondary oscillation. I, therefore, used for some
experiments a secondary circle of 17*5 cm. radius, and a
primary oscillation of the same periodic time as this circle.
The primary oscillator was placed at a distance of 8-9 metres
from the wall. It is, however, difficult to work with apparatus
of such small dimensions. Not only are the sparks exceedingly
minute but the phenomena of resonance, etc., are very feebly
developed. I suspect that oscillations of such rapidity are
very rapidly damped. Thus it was not possible here to make
out as much detail as in the case of the larger circle ; but the

^ [See Note 19 at end of book.]

134 ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION viii

main features, such as those first described above, could be
plainly recognised. Near the wall, and at distances of 2*5
and 4'5 metres from it, the stronger sparks were on the side
next the wall; at the intermediate positions (1*5 and 3*5
metres from the wall) the stronger sparks were on the side
next the primary oscillation. A change of sign occurred about
every metre ; accordingly the half wave-length was here only
2 metres, and the oscillation was more than twice as rapid as
that first used.

Finally, I may remark that as far as the above experiments
are concerned, no great preparations are essential if one is
content with more or less complete indications of the
phenomena. After some practice one can find indications of
reflection at any wall. Indeed, the action of the reflected
waves can be quite well recognised between any one of the
iron pillars above referred to and the primary oscillation ; and
similarly on the opposite side the electromagnetic shadow can
be perceived.

Let us now extend our experiments in a new direction.
Hitherto the secondary conductor has been placed between the
reflecting wall and the primary oscillation — that is to say, in a
space in which the direct and reflected waves travel in opposite
directions and by interference produce stationary waves. If, on
the contrary, we place the primary oscillation between the wall
and the secondary conductor, the latter is situated in a space
in which the direct and reflected waves travel in the same
direction. Hence these must combine to produce a progressive
wave, the intensity of which will, however, depend upon the
difference of phase between the two interfering waves. If the
phenomena are to be at all striking, the two waves must be of ^

similar intensity ; hence the distance of the primary oscillation
from the wall must not be large compared with the dimensions
of the latter, and must be small compared with the distance from
the secondary oscillation. In order to test whether the cor-
responding phenomena could be observed under the working
conditions, I arranged an experiment as follows: — The secondary J

circle was now set up at a distance of 14 metres from the reflect-
ing wall, and therefore 1 metre away from the opposite wall. Its ]
plane was parallel to what we have called the plane of oscilla-
tion, and its spark-gap was turned towards the nearer wall so

VIII ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION 135

that the conditions were specially favourable for the appear-
ance of sparks in it The primary conductor was set up
parallel to its original position in front of the conducting wall,
and at first at a very short distance — about 30 cm. — from it.
The sparks in the secondary circle were extremely feeble. The
spark-gap was now adjusted so that no sparks whatever passed
over. The primary conductor was next shifted step by step
away from the wall. Single sparks soon appeared in the
secondary conductor, and these ran into an unbroken stream of
sparks when the primary conductor arrived at a distance of
1*5-2 metres from the wall — that is to say, at the point B,
This might be referred to the decrease in the distance between
the two conductors. But when I now removed the primary
conductor further away from the wall, and therefore nearer to
the secondary, the sparks again diminished and disappeared when
the primary arrived at C. On proceeding still further the
sparks began to increase and did so now continuously. N"o
exact measurement of the wave-length can be deduced from
these experiments, but from what has been stated above it will
be seen that the wave-lengths already obtained are in accord-
ance with the phenomena. The experiments could be very
well carried out with the smaller apparatus. The primary
conductor was set up at a distance of 1 metre from the wall, and
the corresponding secondary conductor 9 metres from the wall.
The sparks in the latter were certainly small, but could be
quite well observed. They disappeared when the primary
conductor was moved out of its position,* whether it was moved
towards the wall or towards the secondary conductor. The
sparks only reappeared when the distance from the wall was
increased to 3 metres, and from there on they did not again dis-
appear on approaching nearer to the secondary conductor. It is-
worthy of notice that at the same distance of 2 metres the pres-
ence of the wall proved to be of assistance in propagating the
induction in the case of the slower oscillation, whereas it was a
hindrance in the case of the more rapid one. This shows
plainly that the position of the points to which we have drawn
attention is determined by the dimensions of the oscillator, and
not by those of the wall or room.

In acoustics there is an experiment analogous to those
last described, in which it is shown that when a tuning-fork is

136 ELECTROMAGNETIC WAVES IN AIR AND THEIR REFLECTION viii

brought near a wall the sound is strengthened at certain dis-
tances and weakened at others. The analagous experiment in
optics is Lloyd's form of Fresnel's mirror- experiment.^ In
optics and acoustics these experiments count as arguments in
favour of the wave-nature of light and sound; and so the
phenomena here described may be regarded as arguments in
favour of the propagation of the inductive action of an electric
oscillation by wave-motion.

I have described the present set of experiments, as also
the first set on the propagation of induction, without paying
special regard to any particular theory ; and, indeed, the demon-
strative power of the experiments is independent of any
particular theory. Nevertheless, it is clear that the experi-
ments amount to so many reasons in favour of that theory of
electromagnetic phenomena which was first developed by
Maxwell from Faraday's views. It also appears to me that
the hypothesis as to the nature of light which is connected
with that theory now forces itself upon the mind with still
stronger reason than heretofore. Certainly it is a fascinating
idea that the processes in air which we have been investigating
represent to us on a million-fold larger scale the same pro-
cesses which go on in the neighbourhood of a Fresnel mirror
or between the glass plates used for exhibiting Newton's rings.

That Maxwell's theory, in spite of uU internal evidence of
probability, cannot dispense with such confirmation as it has
already received, and may yet receive, is proved — if indeed
proof be needed — by the fact that electric action is not pro-
pagated along wires of good conductivity with approximately
the same velocity as through air. Hitherto it has been inferred
from all theories, Maxwell's included, that the velocity along
wires should be the same as that of light. I hope in time to
be able to investigate and report upon the causes of this
conflict between theory and experiment.^

1 [See Note 20 at end of book.] ^ [gge Note 21 at end of book.]

THE FORCES OF ELECTRIC OSCILLATIONS, TREATED
ACCORDING TO MAXWELL'S THEORY

( fFi€demann*8 Ann. 36, p. 1, 1889.)

The results of the experiments on rapid electric oscillations
which I have carried out appear to me to confer upon Max-
well's theory a position of superiority to all others. Never-
theless, I based my first interpretation of these experiments
upon the older views, seeking partly to explain the phenomena
as resulting from the co-operation of electrostatic and electro-
magnetic forces. .To Maxwell's theory in its pure development
such a distinction is foreign. Hence I now wish to show that
the phenomena can be explained in terms of Maxwell's theory
without introducing this distinction. Should this attempt
succeed, it will at the same time settle any question as to a
separate propagation of electrostatic force, which indeed is
meaningless in Maxwell's theory.

Apart from this special aim, a closer insight into the play
of the forces which accompany a rectilinear oscillation is not
without interest.

The Formvlce

In what follows we are almost solely concerned with the
forces in free ether. In this let X, Y, Z be the components of
the electric force along the co-ordinates ol x, y, z\^ L, M, N,

^ Suppose that you are standing at the origin of the system of co-ordinates
on the a^-plane. Further assume that the direction of positive x is straight in
front, of positive z upwards, and of positive y to the right hand. Unless these
conventions were made, the signs of the electric and magnetic forces in the sub-
sequent equations would not have their usual meanings.

138

THE FORCES OF ELECTRIC OSCILLATIONS

the corresponding components of the magnetic force, both being
measured in Gauss units ; ^ and let t denote the time and A
the reciprocal of the velocity of light. Then, according to
Maxwell, the time-rate of change of the forces is dependent
upon their distribution in space as indicated by the following
equations : —

(1)

f A^^^

'^dt

~'dz

^dt

dX
dz

dZ
dx

dJU

['^dt

(2)

dX tffll rfN
A -— = ^

dt
dY

dz
dN

A-TT- = -T--

dt
dZ

dx
dL

A— = ^--

dy
dL

dz
dM

dt dy dx

Originally, and therefore always, the following conditions
must be satisfied : —

r^L dM dN__^ . dX rfY dZ _^

.J^ ^y ^^ * ^^ ^y ^^

The electric energy contained in a volume-element r of
the ether is equal to 3— / (X^ + Y^ + Z?)dT ; the magnetic energy

is equal to ^— f (^^ + M^ -h N^)rfT, the integration extending

through the volume t. The total energy is the sum of both
these portions.

These statements form, as far as the ether is concerned,
the essential parts of Maxwell's theory. Maxwell arrived at
them by starting with the idea of action -at -a- distance and
attributing to the ether the properties of a highly polarisable
dielectric medium. We can also arrive at them in other
ways. But in no way can a direct proof of these equations be
deduced from experience. It appears most logical, therefore,
to regard them independently of the way in which they have
been arrived at, to consider them as hypothetical assumptions,
and to let their probability depend upon the very large
number of natural laws which they embrace. If we take up

^ H. V. Helmholtz, Wied. Ann, 17, p, 48, 1882.

IX TREATED ACCORDING TO MAXWELL'S THEORY 139

this point of view we can dispense with a number of auxiliary
ideas which render the understanding of Maxwell's theory
more difficult, partly for no other reason than that they really
possess no meaning,^ if we finally exclude the notion of direct
action-at-a-distance.

Multiply equations (1) by L, M, N, and equations (2) by
X, Y, Z ; add the equations together and integrate over a volume
of which dr is the volume-element and dto the surface-element.
We thus get —

d
di

I — J(X2 + Y2 + Z^)dT + - j{U + M2 + W)dT I
= -^| I NY-MZ) cos ?i;» + (LZ-NX) cos n,y\

+ (MX — LY) cos n,z > day,

where n^ n,y np: denote the angles which the normals from
day make with the axis.

This equation shows that the amount by which the energy
of the space has increased can be regarded as having entered
through the elements of the surface. The amount which enters
through each element of the surface is equal to the product of
the components of the electric and magnetic forces resolved
along the surface, multiplied by the sine of the angle which
they form with each other, and divided by 47rA. It is well
known that upon this result Dr. Poynting has based a highly
remarkable theory on the transfer of energy in the electro-
magnetic field.^

With regard to the solution of the equations we restrict
ourselves to the special but important case in which the dis-
tribution of the electric force is symmetrical about the 2;-axis,
in such a way that this force at every point lies in the
meridian plane passing through the axis of z and only
depends upon the 2;-co-ordinate of the point and its distance
p = s/x^ + 3/2 from the 2;-axis. Let E denote the component
of the electric force in the direction of />, namely Xxjp + ^yjp ;
and further let P denote the component of the magnetic force

^ As an example I would mention the idea of a dielectric-constant of the ether.
2 J. H. Poynting, Phil Trans., 1%U, 11. p. 343.

140 THE FORCES OF ELECTRIC OSCILLATIONS ix

perpendicular to the meridian plane, namely liy/p—Mx/p,
We then assert that if '11 is any function whatever of p, z, t,
which satisfies the equation —

X^dmjdfi = AH,

and if we put Q = pdll/dp, then the system

. pZ = dQ/dp, pT = AdQ/dt,

/)E = - dQ/dz, N =

is a possible solution of our equations.

In order to prove this assertion, we observe that we have —

dp _ cm dp _ d^U

dx dx dz dy dy dt

dp __dm dp d^n

~~ dy dy dz ^ dx dx dt

1 d / dU\ dm dm

_l a f »11\ _ <^^11 «^11 ^
o do\ do y dx^ dv^

p dp\ dp J dx^ dy

We have only to substitute these expressions in the
equations (1), (2) and (3) to find equations (2) and (3) identi-
cally satisfied, and also equations (1) if we have regard to the
differential equation for IT.

It may also be mentioned that conversely, neglecting
certain limitations of no practical importance, every possible
distribution of electric force which is symmetrical about the z-
axis can be represented in the above form ; but for the purpose
of what follows it is not necessary to accept this statement.

The function Q is of importance to us. For the lines in
which the surface of revolution Q = const, cuts its meridian
planes are the lines of electric force; if we construct these
for every meridian plane at any instant we get a clear
representation of the distribution of the force. If we cut
the cup-shaped space lying between the surfaces Q and Q + ^Q
in various places by surfaces of rotation around the 2;-axis, then
for all such cross-sections the product of electric force and cross-
section, which Maxwell calls the induction across the section,
is the same. If we arrange the system of surfaces Q = const,
so that in passing from one to another Q increases by the
same amount ^Q, then the same statement holds good if we

IX TREATED ACCORDING TO MAXWELL*S THEORY 141

compare amongst themselves the cross-sections of the various
spaces thus formed. In the plane* diagram formed by the
intersection of the meridian planes with the equidistant surfaces
Q = const., the electric force is only inversely proportional to
the perpendicular distance between two of the lines Q = const,
when the points compared lie at the same distance from the
Z'Sixis ; in general, the rule is that the force is inversely pro-
portional to the product of this distance, and of the co-ordinate
p of the point under consideration.

In what follows we shall introduce along with p and z the
polar co-ordinates r and 0, which are connected with the
former by the relations p = r sin 0, z = r cos ; r then denotes
the distance from the origin of our system of co-ordinates.

The Forces around a Rectilinear Oscillation

Let E denote a quantity of electricity, / a length, m = irjx
the reciprocal of a length, and n = tt/T the reciprocal of a time.
Let us put

This value satisfies the equation A^d^Tl/dfi = AIT, if we
stipulate that m/n = T/\ = A, and hence that \/T shall be
equal to the velocity of light. And it must be noticed that
the equation referred to is satisfied everywhere, except at the
origin of our system of co-ordinates.

In order to find out what electrical processes at this point
correspond to the distribution of force specifted by 11, let us
investigate its immediate neighbourhood. Thus let r be
vanishingly small compared with X, and mr negligible compared
with nt Then 11 becomes^ equal to — E/sin?i^/r. Now
since

\dx^ dy^)
we have

^^^+^-^ Q=-SC>

X = ^d^U/dxdz, Y = - dm/dydz, Z = —d^n/dzdz.

1 [See Note 22 at end of book.]

^ OF THE '

-DNIVERSII

142 THE FORCES OF ELECTRIC OSCILLATIONS ix

Thus the electric forces appear here as the derivatives of a

potential —

dTl ^, . d /1\

S = -;— = — EZ Sin ^^^ , I - ),
^ dz dz \r/

and this corresponds to an electrical double-point, whose axis
coincides with the 2;-axis, and whose moment oscillates between
the extreme values +EZ and — EZ with the period T. Hence
our distribution of force represents the action of a rectilinear
oscillation which has the very small length /, and on whose
poles at the maximum the quantities of electricity + E and— E
become free. The magnetic force perpendicular to the direction
of the oscillation and in its immediate neighbourhood comes

out as —

P = AEIn cos nt sin 0/r^.

According to the Biot-Savart law this is the force of a
current-element of length I lying in the direction of the axis
of Zy and whose intensity, in magnetic measure, oscillates
between the extreme values H-ttAE/T and — ttAE/T. In
fact, the motion of the quantity of electricity E determines a
current of that magnitude.

From n we get —

Q = E/m-^ cos (mr — nt) ^^ ^ >-sm^^,

(^ mr J

and from this the forces Z, E, P follow by differentiation.
Now it is true that the formulae in general turn out to be too
complicated to allow of a direct survey of the distribution of
the forces. But in some special cases, which we will now
indicate, the results are comparatively simple —

(1) We have already considered the immediate neighbour-
hood of the oscillation.

(2) In the 2;-axis, i.e. in the direction of the oscillation, we
have dp = rdffy dz = dr, ^ = ; so that here

E=0, P = 0,

2E/7/1

Z =

f , " sin (mr'—nt)\
i cos [mr — nt) -^ v

\ mr J

The electric force acts always in the direction of the
oscillation ; at small distances it diminishes as the inverse

IX TREATED ACCORDING TO MAXWELL'S THEORY 143

cube, at greater distances as the inverse square, of the
distance.

(3) In the ir^-plane, i.e. when 2;= 0, we have dz= — rdd,
dp = dr, ^ = 90® ; and therefore —

AElmn ( . . ^\ . cos (mr — Tit) '
p = -{ sin (mr-^nt) + — ^ "^

^7' (^ mr

E=0,

EZm^ r • / .\ cos (mr — nt) sin (mr — nt)

Z = i —sm (mr — n^) -^ -a ^^ ^

r [ mr mh"^

In the equatorial plane through the oscillation the electric
force is parallel to the oscillation, and its amplitude is

EZ >,/ 1 — m V + m^r^/r^. The force diminishes continuously
with increasing distance, at first rapidly as the inverse cube,
but afterwards only very slowly and inversely as the distance
itself. At greater distances the action of the oscillation can
only be observed in the equatorial plane, and not along the
axis.

(4) At very great distances we may neglect higher powers
of 1/r as compared with lower ones. Thus we have at such
distances —

Q = EZm cos {mr — nt) sin^^,

from which we deduce —

P = A . 'Elmn sin (mr — nt) sin^/r,
Z = — Wm^ sin (mr — n^) sin^O/r,
E = ISilm^ sin (mr — nt) sinO cos0/r.

Whence it follows that Z cos ^ + E sin^= 0. Hence at
great distances the force is everywhere perpendicular to the
radius vector from the origin of the force; the propagation
takes place in the form of a pure transversal wave. The
magnitude of the force is EZm^ sin (mr — nt) sinO/r. At a
constant distance from the zero-point it decreases towards the
axis, being proportional to the distance from the latter.

In order now to find the distribution of force in the
remaining parts of space we make use of graphic representa-
tion, drawing for definite times the lines of electric force, i.e,
the curves Q = const., for equidistant values of Q. Since Q
appears as the product of two factors, of which the one

144

THE FORCES OF ELECTRIC OSCILLATIONS

depends only upon r, and the other only upon 0, the con-
struction of these curves presents no great diflBculty. We

split up each value of Q, for which we wish to draw the
curve, in various ways into two factors; we determine the
angle 6 for which sin^^ is equal to the one factor and, by

TREATED ACCORDING TO MAXWELL'S THEORY

145

means of an auxiliary curve, the value of r for which the
function of r contained in Q is equal to the other factor ; in

this way we find as many points on the curve as we please.
On setting about the construction of these curves one perceives
many small artifices which it would be tedious to exhibit here.

I 146 THE F0RCE8 OF ELECTRIC OSCILLATIONS ix

We shall content ourselves with considering the results of the
construction as shown in Figs. 27-30. These figures exhibit
the distribution of force at the times ^ = 0, ;^T, ^T, f T,
or by a suitable reversal of the arrows for all subsequent
times which are whole multiples of ^T. At the origin is
shown, in its correct position and approximately to cor-
rect scale, the arrangement which was used in our earlier
experiments for exciting the oscillations. The lines of
force are not continued right up to this picture, for our
formulaB assume that the oscillator is infinitely short, and
therefore become inadequate in the neighbourhood of the finite
oscillator.

Let us begin our explanation of the diagrams with Fig. 27.
Here ^ = ; the current is at its maximum strength, but the
poles of the rectilinear oscillator are not charged with elec-
tricity — no lines of force converge towards them. But from
the time ^ = onwards, such lines of force begin to shoot out
from the poles ; they are comprised within a sphere repre-
sented by the value Q = 0. In Fig. 27, indeed, this sphere is
still vanishingly small, but it rapidly enlarges, and by the
time^ = :jT (Fig. 28) it already fills the space B^. The
distribution of the lines of force within the sphere is nearly of
the same kind as that corresponding to a static electric charge
upon the poles. The velocity with which the spherical surface
Q =» spreads out from the origin is at first much greater than
1/A; in fact, for the time |-T this latter velocity would only
correspond to the value of ^X given in the figure. At an
infinitesimal distance from the origin the velocity of propagation
is even infinite. This is the phenomenon which, according to
the old mode of expression, is represented by the statement that
upon the electromagnetic action which travels with the velocity
1/A, there is superposed an electrostatic force travelling with
infinite velocity. In the sense of our theory we more correctly
represent the phenomenon by saying that fundamentally the
waves which are being developed do not owe their formation
solely to processes at the origin, but arise out of the conditions
of the whole surrounding space, which latter, according to our
theory, is the true seat of the energy. However this may be,
the surface Q = spreads out further with a velocity which
gradually sinks to 1/A, and by the time t = ^T (Fig. 29) fills

IX TREATED ACCORDING TO MAXWELL'S THEORY 147

the space B^. At this time the electrostatic charge of the
poles is at its greatest development ; the number of lines of
force which converge towards the poles is a maximum. As
time progresses further no fresh lines of force proceed from the
poles, but the existing ones rather begin to retreat towards the
oscillating conductor, to disappear there as lines of electric
force, but converting their energy into magnetic energy. Here
there arises a peculiar action which can plainly be recognised,
at any rate in its beginnings, in Fig. 30 (< = ;|T). The lines
of force which have withdrawn furthest from the origin become
laterally inflected by reason of their tendency to contract
together ; as this inflection contracts nearer and nearer towards
the 2;-axis, a portion of each of the outer lines of force detaches
itself as a self- closed line of force which advances indepen-
dently into space, while the remainder of the lines of force sink
back into the oscillating conductor.

The number of receding lines of force is just as great as
the number which proceeded outwards, but their energy is
necessarily diminished by the energy of the parts detached.
This loss of energy corresponds to the radiation into space.
In consequence of this the oscillation would of necessity soon
come to rest unless impressed forces restored the lost energy
at the origin. In treating the oscillation as undamped, we
have tacitly assumed the presence of such forces. In Fig. 27
— to which we now return for the time ^ = T, conceiving the
arrows to be reversed — the detached portions of the lines of
force fill the spherical space JK^, while the lines of force pro-
ceeding from the poles have completely disappeared. But new
lines of force burst out from the poles and crowd together the
lines whose development we have followed into the space R^
(Fig. 28). It is not necessary to explain further how these
lines of force make their way to the spaces R^ (Fig. 29), JK^
(Fig. 30), i2g (Fig. 27). They run more and more into a pure
transverse wave-motion, and as such lose themselves in the
distance. The best way of picturing the play of the forces
would be by making drawings for still shorter intervals of
time and attaching these to a stroboscopic disk.

A closer examination of the diagrams shows that at points
which do not lie either on the 2;-axis or in the icy-plane the
direction of the force changes from instant to instant. Thus,

148 THE FORCES OF ELECTRIC OSCILLATIONS ix

if we represent the force at such a point in the usual manner
by a line drawn from the point, the end of this line will not
simply move backwards and forwards along a straight line
during an oscillation, but will describe an ellipse. In order to
find out whether there are any points at which this ellipse
approximates to a circle, and in which, therefore, the force turns
successively through all points of the compass without any
appreciable change of magnitude, we superpose two of the
diagrams which correspond to times differing by ^T from one
another, e.g. Figs. 27 and 29, or 28 and 30. At such points
as we are trying to find, the lines of the one system must
clearly cut those of the second system at right angles, and the
distances between the lines of the one system must be equal
to those of the second. The small quadrilaterals formed by
the intersection of both systems must therefore be squares at
the points sought. Now, in fact, regions of this kind can be
observed; in Figs. 27 and 28 they are indicated by circular
arrows^ the directions of which at the same time give the
direction of rotation of the force. For further explanation
dotted lines are introduced which belong to the system of
lines in Figs. 29 and 30. Furthermore, we find that the
behaviour here sketched is exhibited by the force not only at
the points referred to, but also in the whole strip -shaped
tract which, spreading out from these points, forms the neigh-
bourhood of the 2;-axis. Yet the force diminishes in magnitude
so rapidly in this direction that its peculiar behaviour only
attracts attention at the points mentioned.

In an imperfect series of observations which are not
guided by theory, the force -system here described, and
required by theory, may well exhibit itself in the manner
described in an earlier paper.^ The observations referred
to do not by any means enable us to recognise all the com-
plicated details, but they show correctly the main features
of the distribution. According to both observation and
theory the distribution of the force in the neighbourhood
of the oscillator is similar to the electrostatic distribution.
According to both observation and theory the force spreads
out chiefly in the equatorial plane and diminishes in that
plane at first rapidly, then slowly, without becoming zero

1 See v., p. 90.

IX TREATED ACCORDING TO MAXWELL'S THEORY 149

at any intermediate distance. According to both observa-
tion and theory the force in the equatorial plane, along
the axis, and at great distances, is constant in direction and
variable in magnitude; whereas, at intermediate points, its
direction varies greatly and its magnitude but little. The
only want of accord between theory and the observations
referred is in this — that, according to the former, the force at
great distances should always be perpendicular to the radius
vector from the origin, whereas, according to the latter, it
appeared to be parallel to the oscillation. These two come
to the same thing for the neighbourhood of the equatorial
plane, where the forces are strongest, but not for directions
lying between the equatorial plane and the axis. I believe
that the error is on the side of the observations. In
the experiments referred to the oscillator was parallel to
the two main walls of the room used; and the components
of the force parallel to the oscillator might thereby be
strengthened as compared with the components normal to
the oscillator.

I have therefore repeated the experiments, making various
alterations in the^ position of the primary oscillator, and found
that in certain positions the results were in accordance with
theory. Nevertheless, the results were not free from ambiguity,
for at great distances and in places where the force was feeble,
the disturbances due to the environment of the space at my
disposal were so considerable that I could not arrive at a
trustworthy decision.

While the oscillator is at work the energy oscillates in and
out through the spherical surfaces surrounding the origin. But
the energy which goes out during each period of oscillation
through every surface is greater than that which returns, and
is greater by the same amount for all the surfaces. This
excess represents the loss of energy due to radiation during
each period of oscillation. We can easily calculate it for a
spherical surface, whose radius r is so great that we may use
the simplified formulae. Thus the energy which goes out in
the element of time dt through a spherical zone lying between
^ and ^ + de is

dt . 27rr sin ^ . rcZ^ . (Z sin ^ - R cos &) P . \\4tirK.

150 THE FORCES OF ELECTRIC OSCILLATIONS ix

K we here substitate for Z, P, R, the values corresponding
to large values of r and integrate with respect to from to tt,
and with respect to t from to T, we get for the energy which
goes out through the whole sphere during a half-oscillation

Let us now try to deduce from this an approximate
estimate of the quantities actually involved in our experi-
ments. In these we charged two spheres of 15 cm. radius in
opposite senses up to a sparking distance of about 1 cm. If
we estimate the difference of potential between the two spheres
as 120 'C.G.S. electrostatic units (gm.* cm.* sec ~^), then each
sphere was charged to a potential of ± 60 C.G.S. units, and
therefore its charge was E=15x60 = 900 C.G.S. units
(gm.* cm.^ sec.~^). Hence the whole stock of energy which the
oscillator possessed at the start amounted to 2x^x900x60
= 54,000 ergs, or about the energy which a gramme- weight
would acquire in falling through 55 cm. The length I of the
oscillator was about 100 cm., and the wave-length about
480 cm. Hence it follows that the loss of energy in the half-
period of oscillation was about 2400 ergs.^ It is therefore
evident that after eleven half-oscillations one-half of the energy
will have been expended in radiation. The rapid damping of
the oscillations, indicated by our experiments, was therefore neces-
sarily determined by the radiation, and would still occur even if
the resistance of the conductor and of the spark became negligible.

To furnish energy amounting to 2400 ergs in 1*5 hundred-
millionths of a second is equivalent to working at the rate of
22 horse-power. The primary oscillator must be supplied with
energy at fully this rate if its oscillations are to be kept up
continuously and with constant intensity in spite of the radia-
tion. During the first few oscillations the intensity of the
radiation at a distance of about 12 metres from the primary
conductor corresponds to the intensity of the sun's radiation at
the surface of the earth.

The InterfereTvce-Experiments

In order to ascertain the velocity of propagation of the
electric force in the equatorial plane, we caused it to interfere

^ [See Note 23 at end of book.]

IX TREATED ACCORDING TO MAXWELL'S THEORY 151

with the action of an electric wave proceeding with constant
velocity along a wire.^ It appeared that the resulting inter-
ferences did not succeed each other at equal distances, but
that the changes were more rapid in the neighbourhood of the
oscillation than at greater distances. This behaviour was
explained by the supposition that the total force might be
split up into two parts, of which the one, the electromagnetic,
was propagated with the velocity of light, while the other,
the electrostatic, was propagated with a greater, and perhaps
infinite velocity. But now, according to our theory, the force
under consideration in the equatorial plane is —

Z = EZmS

sin {mr — nt) cos {mr — nt) sin(mr — nt)

and this expression can in no way be split up into two simple
waves travelling with different velocities. Hence if our present
theory is correct, the earlier explanation can only serve as an
approximation to the truth. Let us now investigate whether
the present theory leads to any explanation of the phenomena.
To begin with, we can write Z = B sin (nt — S^), where the

amplitude of the force B = E^v 1— wiV + ^V/r^, and the
phase Sj of the force is determined by the equation —

^ __ sin mr/mr + cos mrjm^T^ — sin mr/m^r^

Lan o^ — . ; J ,

cos mrjmr — sin mrlmh^ — cos mr/m^
which, after transformation, gives

= mr — tan ^

^ 1 — m^r^

In Fig. 31 the quantity B^ is represented as a function of
mr by the curve S^, The length a & in the figure corresponds
to the value of tt, both for abscissae and ordinates. If we
regard r, instead of mr, as the variable abscissa, the length a b
in the abscissae corresponds to the half wave-length. For the
purpose of referring directly to the experiments which we wish
to discuss, there is placed beneath the diagram a further
division of the axis of abscissae into metres. According to the
results obtained by direct experiment^ \ is put = 4*8 metres, and

1 See VII., p. 107. 2 gg^ VIII., p. 124.

152

THE FORCES OF ELECTRIC OSCILLATIONS

from this the length of the metre (or scale of divisions) is
determined ; but the first mark of the divided scale is not at
the oscillator, but is placed at a distance of 0*45 metre beyond
the latter. In this way the divisions represent the divisions

Fig. 31.

of the base-line which we used in determining the interferences.
We see from the figure that the phase does not increase from
the source ; its course is rather as if the waves originated at
a distance of about ^X in space and spread out thence, partly
towards the conductor, and partly into space. At great
distances the phase is smaller by the value tt than it would
have been if the waves had proceeded with constant velocity
from the origin ; the waves, therefore, behave at great distances
as if they had travelled through the first half wave-length with
infinite velocity.

The action w of the waves in the wire for a given position
of the secondary conductor can now be represented in the form
w = G sin (nt — S^, wherein S^ is used as an abbreviation for
m^r + 8 = 7rr/\ + B. \ denotes the half wave-length of the
waves in the wire, which in our experiments was 2*8 metres.
B indicates the phase of its action at the point r = 0, which
we altered arbitrarily by interposing wires of various lengths.
Similarly we were able to alter the amplitude C, and we made
it of such magnitude that the action of the waves in the wire
was approximately equal to the direct action. The phase of

IX TREATED ACCORDING TO MAXWELL'S THEORY 153

the interference then depends only upon the difference between
the phases S^ and B^. With that particular adjustment of the
secondary circle to which our expression for w relates, both
actions reinforce one another (i.e. the interference has the
sign + ) if Sj — Sg is equal to zero or an odd multiple of
27r; the actions annul one another (i,€. the interference has
the sign — ) if S^ — Sg is equal to tt or an odd multiple of it ;
no interference takes place (the interference has the sign 0) if
Sj — Sg is equal to an odd multiple of ^tt.

Let us now suppose that S is so determined that, at the
beginning of the metre-scale, the phase of the interference has
a definite value e, so that B^ = B^ + e. The straight line 1 in
our figure will then represent the value of Sg + e as a function
of the distance. For the inclination of the line is so chosen that
for an increase of abscissa by X^ = 2*8 metres, the ordinate
increases by the value ir ; and it is so placed that it cuts the
curve Sj at a point whose abscissa is at the beginning of the
metre-scale. The lines 2, 3, 4, etc., further represent the
co^uafi q£ the values of S,^ + € — ^tt, S^ + e — ir, S^ + e — f tt,
etc. For these lines are parallel to the line 1, and are so drawn
that they cut any given ordinate at distances of ^, and any
given abscissa at distances of 1*4 metre. If we now project the
points of intersection of these straight lines with the curve B^
upon the axis of abscissae below, we clearly obtain those
distances for which B^ is equal to S^ + e + ^ir, B^ + e + iTy
B^ + € + 1^, etc., i.e. for which the phase of the interference
has increased by ^tt, tt, I^tt, etc., as compared with the zero-
point. We thus deduce directly from the figure the following
statements : — If at the zero-point of the base-line the inter-
ference has the sign -|- ( — ), it first attains the sign at about
1 metre, the sign ~ ( + ) at about 2*3 metres, and it again
acquires the sign at about 4*8 metres : the interference
reverts to the sign + ( — ) at about 7*6 metres, is again at
about 14 metres, and from there on the signs succeed each
other in order at about equal distances. If at the zero-point
of the base-line the interference has the sign 0, it will also
have this sign at about 2*3 metres, 7*6 metres, and 14 metres ;
it will have a marked positive or negative character at about
1 metre, 4*8 metres, and 11 metres from the zero-point.
Intermediate values correspond to intermediate phases. If this

154 THE FORCES OF ELECTRIC OSCILLATIONS ix

theoretical result is compared with the experimental result, and
especially with those interferences which occurred on introducing
100, 250, 400, and 550 cm. of wire,^ the accordance will be
found as complete as could possibly be expected.

I have not been able to account so well for the inter-
ferences of the second kind.^ For producing these interferences
we used the secondary circle in a position in which the most
important factor was the integral force of induction around
the closed circle. If we regard the dimensions of the latter as
vanishingly small, the integral force is proportional to the rate
of change of magnetic force perpendicular to the plane of the
circle, and is therefore proportional to the expression —

( mr m^r^ J

Hence we deduce the phase S^ of this action —

cs cos mr/mr — sin mrlm^r^

tan e„= '- — y o>

sin mr/mr + cos mrjm^'r

or, after transformation —

S3 = mr — tan"~^ mr.

The line Sg of Fig. 31 represents the course of this function.
We see that the phase of this action increases continuously
from the origin itself. Hence the phenomena which point to
a finite rate of propagation must, in the case of these inter-
ferences, make themselves felt even close to the oscillator.
This was indeed apparent in the experiments, and therein lay
the advantage presented by this kind of interference. But,
contrary to the experiment, the apparent velocity near to the
oscillator comes out greater than at a distance from it ; and
it cannot be denied that, according to theory, the change of
phase of the interference should be slightly, but noticeably,
more rapid than it was in the experiments. It seems to me
probable that a more complete theory — in which the two con-
ductors used would not be regarded as vanishingly small, —
and perhaps a different estimate of the value of \, would
establish a more satisfactory agreement.

1 See p. 118. * See p. 119.

IX TREATED ACCORDING TO MAXWELL'S THEORY 155

It is, however, important to notice that even on the basis of
Maxwell's theory, the numerical results obtained cannot be ex-
plained without assuming a considerable diflference between the
rates of propagation of the waves in wires and in free space.

Waves in Wire-shaped Condicctars
The function K{pp) = |r-*^p(e«+e-^'>^w,

which, fox large values of p, approximates asymptotically to the

function s/'^/^PP • ^ ^^* ^^^ ^^^ infinitesimal values of p to the
function — log (j>p/2) — 0'5 7 7,satisfies the differential equation —

dp^ p dp
If we therefore put —

11 = — . sin {mz — nt) . 'K{pp),

then n satisfies the equation A^d^Hjdt^ = ATI, if we make
2j^ = m^ — AW. Here J must be understood to represent
a current expressed in magnetic measure, p and m — ir/X
reciprocals of lengths, and n = tt/T the reciprocal of a time.
The function 11 satisfies its equation through all space, except
along the z-axis, where it is discontinuous. The values
R, Z, P, N, which can be deduced from the above 11, represent
therefore an electrical disturbance taking place in a very thin
wire stretched along the 2!-axis. In the immediate neighbour-
hood of this wire, neglecting quantities which contain even
powers of p, we have —

and therefore —

Qa = — -r- • sin (mz'—nf),
An

-p. 2Jm . .

Eq = . cos {mz — nt),

Anp

Pq = — .cos {mz — nt),
P

in which the suffix indicates that p is assumed to be

156 THE FORCES OF ELECTRIC OSCILLATIONS tx

vaitisbingly smalL From the expression for K^ it follows that
the gnantity of free electricity c in unit length of the wire is —

e = — . lira . K. = - . cos (mz — nt).
4w " An

Similarly from the expression for P^, it follows that the
current i is —

i= ■- . 2vp . P. = J cos {mz — rU).

The values of i and e satisfy of themselves the necessary
equation Adejdt= —dijdz. They show as that the disturb-
ance under consideration is an electric sine-wave which is
propagated in the positive direction along the axis of 2, whose
half wave-length is X, and half-period of oscillation T, whoso
velocity ia therefore X/T = njm,, and whose intensity is such
that the maximum current which arises is -t J.

If we stipulate that external forces niay be made to act
arbitrarily in the wire, we may regard X and T as being inde-
pendent of each other. For every given relation between these
quantities, te. for every given velocity of the waves, the lines
of electric force have a definite form which, independently of
time, glides along the wire. As before, we represent this form,
drawing the lines Q = const.

Such a representation is carried out in Fig. 32. In the
first place. Fig. 32g represents the case in which the velocity is
very small and thereforej? = ?«. The drawing then represents
a distribution of electrostatic force, viz. that which is obtained
when we distribute electricity upon the wire so that its density

IX TREATED ACCORDING TO MAXWELL'S THEORY 157

is a sine-function of the length of the wire. Fig. 32^ gives
the lines of force for a velocity amounting to nearly 28/48 of
that of light. We see that in proceeding from and returning to
the wire the lines of force make a wider circuit than before.
According to the older mode of conception, this would be
explained by saying that the electromagnetic force, which is
parallel to the wire, weakens the component of the electrostatic
force in the same direction, whereas it does not affect the
component perpendicular to the wire. The weakening of the
component parallel to the wire may even amount to annulling
it altogether. For if we take the velocity of propagation of the
wire-waves as being equal to that of light, p becomes zero,
K{pp) reduces to — log /> + const, for every value of p, and
for every value of p —

Q = . sin (viz — nt)y

and therefore-

E = . cos (mz — nt), Z = 0,

Anp

2J
P = — .cos (mz — nt), N = 0.

The distribution of force then is the simplest that can be
conceived ; the electric force is everywhere normal to the wire
and decreases in inverse proportion to the distance from it.
The lines Q = const, drawn for equidistant values of Q, are
represented in Fig. 32^. For waves travelling with a velocity
greater than l/A, p becomes imaginary. For this case our
formulae would require transformation, but as it has no practical
significance, we need not discuss it.

At the surface of a conductor, that component of the elec-
tric force which is tangential to the surface continues without
discontinuity in the interior of the conductor. According to
Maxwell, a perfect conductor is understood to mean one in
whose interior there can only exist vanishingly small forces.
From this it necessarily follows that at the surface of a perfect
conductor the components of the force tangential to the surface
must vanish. Unless this statement is incorrect, it follows
that electric waves in wires of good conductivity must be
propagated with the velocity of light and in the form which is

158 THE FORCES OF ELECTRIC OSCILLATIONS ix

represented in Fig. 32^. For only in this particular force-
distribution is the force everywhere normal to the surface of
the wire. In fact, then, it follows from Maxwell's theory,
as well as from the older theories, that electric waves travel
along perfectly conducting wires with the velocity of light

If, on the other hand, we are to place any reliance upon
our experiments, this conclusion is incorrect — ^the propagation
takes place with a much smaller velocity and in some such
form as is indicated in Fig. 32,^. The result is all the more
remarkable, because the velocity in wires appears likewise to
be a velocity which is quite independent of the nature of the
wire. I have found it to be the same in wires of the most
diverse metals, varying widely in thickness and in the shape
of their cross-section, and also in columns of conducting
fluids. The causes which determine this velocity still remain
obscure. The resistance, at all events, has nothing to do with
it. For some time I thought that it might be affected by the
constant A, through the introduction of which Hr. H. v.
Helmholtz has extended Maxwell's theory ; ^ but further con-
sideration led to the rejection of this idea. If only the
limiting condition were correct, a wave of the form of Fig.
32c would yet be possible. This would always be a pure
transversal wave, and as such must travel with the same
velocity as plane transversal waves in space, whether simul-
taneous longitudinal waves are possible or not. Although a
finite value of the constant h would not explain the difference
between the two velocities, it would postulate the possibility
of two kinds of waves in the wire with different velocities :
experiment has hitherto given no intimation of such a pheno-
menon. It seems rather to be doubtful whether the limiting
condition is correct for rapidly alternating forces.

Although it does not appear to be possible, on the one hand,
to confer a velocity of any desired magnitude upon the waves
travelling along the 2;-axis, there is no difi&culty, on the other
hand, in reducing the velocity as much as may be desired below
its maximum value, or in producing distributions of force
intermediate between the forms 32^ and 32|,. With this
object the waves are made to proceed along crooked wires or
wires rolled into spirals. For example, I rolled a wire 40 metres

^ H. V. Helmholtz, (}es, Abh, 1, p. 545.

IX TREATED ACCORDING TO MAXWELL'S THEORY 159

long into a spiral 1 cm. in diameter, and so tightly that the
length of the spiral was 1*6 metre ; in this I was able to observe
nodes at distances of about 0*31 metre, whereas, in the straight
wire, the nodes were 2*8 metres apart. As the spiral was stretched
out, the one value changed gradually into the other. Hence,
when the velocity is measured along the 2;-axis (the axis of
the spiral), the wave moves much more slowly in the coiled
wire. When the velocity is measured along the wire itself,
on the other hand, the wave certainly moves more rapidly.
Along crooked wires the behaviour is similar. Unless I
am mistaken. Maxwell's theory, assuming the limiting con-
dition for good conductors, is unable to account " for this.
It seems to me that according to this theory the propagation,
measured along the 2;-axis, must for every form of conductor
take place with the velocity of light ; provided, in the first place,
that the resistance of the conductor does not come into con-
sideration, and, in the second place, that the dimensions of the
conductor perpendicular to the axis are negligible in comparison
with the wave-length. Both conditions are satisfied by coiled
metallic wires ; but what should happen does not happen.

In our endeavour to explain the observations by means of
Maxwell's theory, we have not succeeded in removing all
difi&culties. Nevertheless, the theory has been found to account
most satisfactorily for the majority of the phenomena ; and it
will be acknowledged that this is no mean performance. But
if we try to adapt any of the older theories to the phenomena,
we meet with inconsistencies from the very start, unless we
reconcile these theories with Maxwell's by introducing the
ether as dielectric in the manner indicated by v. Helmholtz.

ON THE PROPAGATION OF ELECTRIC WAVES

BY MEANS OF WIRES

( Wiedemann* 8 Ann. 37, p. 395, 1889.)

When a constant electric current flows along a cylindrical
wire, its strength is the same at every part of the section of
the wira But if the current is variable, self-induction pro-
duces a deviation from this most simple distribution. For the
central parts of the wire are, on the whole, less distant from
all the rest than are the outer parts ; hence induction opposes
variations of the current in the centre of the wire more strongly
than at the circumference, and consequently the current by
preference flows along the outer portion of the wire. When
the current changes its direction a few hundred times per
second, the deviation from the normal distribution can no
longer be imperceptible. This deviation increases rapidly
with the rate of alternation ; and when the current alternates
many million times per second, almost the whole of the interior
of the wire must, according to theory, appear free from
current, and the flow must confine itself to the very skin of
the wire. Now in such extreme cases the above conception of
what takes place is obviously not free from physical diflSculties ;
and preference must be given to another conception of the
matter which was first presented by Messrs. 0. Heaviside ^ and
J. H. Poynting,^ as the correct interpretation of Maxwell's
equations as applied to this case. According to this view, the
electric force which determines the current is not propagated

^ 0. Heaviside, Electrician, January 1885, Phil. Mag. 25, p. 153, 1888.
2 J. H. Poynting, Phil. Trans. 2, p. 277, 1885.

X PROPAGATION OF ELECTRIC WAVES BY WIRES 161

in the wire itself, but under all circumstances penetrates from
without into the wire, and spreads into the metal with com-
parative slowness and according to laws similar to those which
govern changes of temperature in a conducting body. Thus
when the forces around the wire continually alter their
direction, the action of these forces only extends to a very
slight depth within the metal ; the slower the fluctuations, the
more deeply will the action penetrate ; and lastly, when the
changes succeed each other with infinite slowness, the force
has time to penetrate into the interior of the wire and to act
with uniform strength throughout it.^

Whatever conception we may form from the theoretical
results, it is important to find out whether these latter agree
with the actual facts. Inasmuch as I made use of electric
waves in wires of exceedingly short period in my experiments
on the propagation of electric force, it was natural to test by
means of these the correctness of the conclusions deduced. As
a matter of fact the theory was found to be confirmed by the
experiments which are now to be described ; and it will be
seen that these few experiments are amply sufi&cient to support
the conception introduced by Messrs. Heaviside and Poynting.
Similar experiments, with similar results, have been carried out
by Dr. O. J. Lodge,^ who has, however, used quite different
experimental methods, and mainly with the object of elucidating
the theory of lightning-conductors. To what extent the con-
clusions are true which were deduced by Dr. Lodge in the
latter respect from his experiments must, in the first place,
depend upon the actual rapidity of succession of the changes
of electrical conditions which accompany lightning.

The apparatus and methods which are here mentioned are
those which have been fully described in my previous papers.
The waves used were such as had in wires nodes about 3
metres apart.

1. When a primary conductor acts through air upon
a secondary conductor, there can be no doubt that the
action penetrates from without into the latter. For it may
be regarded as an established fact that in air the action is
propagated from point to point, and it must therefore first meet

* [See Note 24 at end of book.]
3 0. J. Lodge, Joum. of Soc, of Arts, May 1888 ; Phil. Mag. 26, p. 217, 1888.

162 PROPAGATION OF ELBCTRIC WAVES BY WIRES x

the outer boundary of the conductor before it can act upon the
inside. Now it can be shown that a closed metallic envelope
does not allow the action to pass through it at all. If we
place the secondary conductor in a favourable position with
reference to the primary so that sparks 5-6 mm. long are
obtained, and then surround it with a closed box of sheet
zinc, not the slightest amount of sparking can be detected.
Similarly the sparks disappear when the primary conductor is
completely surrounded by a metal box. It is known that a
metal screen does not interfere with the integral force of
induction when the fluctuations of current are relatively slow.
At first sight this appears to contradict the above experimental
results. But the contradiction is only apparent and disappears
when the time-relations are considered. In a similar way a
badly -conducting envelope protects its interior completely
against rapid fluctuations of external temperature, less com-
pletely against slow fluctuations, and not at all against a
permanent rise or fall in temperature. The thinner the
envelope the more rapid are the fluctuations which can act
through it upon the interior. And so in our case also, the
electric action should clearly penetrate into the interior if we
only reduced sufficiently the thickness of the metal. Yet I
did not find it easy to secure the requisite thinness. A box
covered with tinfoil acted as a perfect screen ; and so too did
a box of gilt paper when care was taken to make good contact
between the edges of the separate pieces of paper. In this
case the thickness of the conducting metal could scarcely be
estimated as high as -^ mm. I next fitted the protecting
envelope as closely as possible around the secondary conductor.
For this purpose its spark-gap was drawn out to about 20 mm. ;
and, in order to be still able to detect electric disturbances in
it, an auxiliary spark-gap was introduced just opposite the
usual one. The sparks in this were not so long as in the
proper spark-gap because the resonance-eflect was now absent,
but they still were quite vigorous. After being thus prepared
the conductor was completely surrounded with a tube-shaped
conducting envelope made as thin as possible; this did not
touch the conductor, but was brought as close as possible to it,
and in the neighbourhood of the auxiliary spark-gap — in order
to be able to make use of the latter — was made of wire-gauze.

X PROPAGATION OF ELECTRIC WAVES BY WIRES 163

Between the poles of this envelope the sparking was as vigorous
as it had previously been in the secondary conductor itself ;
but in the enclosed conductor not the slightest electrical
disturbance could be perceived. It does not interfere with the
result if the envelope touches the conductor at a few points ;
it is not necessar}' to insulate the two from one another in
order to make the experiment succeed, but only in order to
give it its demonstrative force. In imagiuation we can clearly
draw the envelope around the conductor more closely than is
possible in practice ; indeed, we can imagine it to coincide with
the outer skin of the conductor. Thus although the electrical
disturbances at the surface of our conductor are so powerful as
to produce sparks of 5-6 mm. length, yet at a depth of only
-^ mm. below its surface there is such complete calm that not
the slightest sparking is produced. We are thus led to suspect
that what we call an induced current in the secondary con-
ductor is a process which takes place for the most part in the
surrounding space and in which the inside of the conductor
scarcely plays any part.

2. We might admit that this is so when an electrical
disturbance passes through a dielectric, but yet maintain that
it is otherwise when the disturbance, as we usually say, has
been propagated in a conductor. Near one of the end plates
of our primary conductor let us place a conducting plate and
fasten to it a long straight wire ; in our earlier experiments we
have already shown how the action of the primary oscillation
can be conveyed to great distances with the aid of such a wire.
The usual view of this is that the wave proceeds through the wire.
We will, however, try to show that all the changes are confined
to the surface and the space outside, and that the interior of
the wire knows nothing of the passing waves. I first arranged
experiments in the following manner. From the conducting wire
a piece 4 metres long was removed and replaced by two strips of
zinc sheet 4 metres long and 10 cm. broad, which were laid flat
one upon the other with their ends touching and firmly con-
nected. Along the whole length of the middle line between
the strips, and hence almost completely surrounded by metal,
was placed a copper wire 4 metres long and covered with gutta-
percha. It made no difference in the experiments whether
the outer ends of this wire were in metallic connection with

164 PROPAGATION OF ELECTRIC WAVES BY WIRES x

the strips, or insulated from them; but generally the ends
were soldered to the zinc strips. The copper wire was cut in
the middle, and its ends were twisted round each other and
led out between the strips to a small spark-gap by which any
electrical disturbance in the wire could be perceived. Not
the slightest action could be detected at the spark-gap, even
when the strongest possible waves were led through the whole
arrangement. But if any part of the copper wire, a few deci-
metres long, was pulled out of its place so as to project but a
little beyond the strips, sparking immediately began. The
longer the projecting part and the further it extended beyond
the edge of the strips, the more vigorous became the sparking.
The absence of sparks in the first instance cannot be attributed
to any unfavourable conditions of resistance; no change has
taken place in these conditions; only the wire at first was
inside a conducting mass and beyond the reach of outside
influences. Indeed, it is only necessary to enclose the pro-
jecting part of the wire with a little tinfoil in metallic
connection with the zinc strips, in order to stop the sparking
at once. By so doing we virtually bring the copper wire
back inside the conductor. In like manner the sparks become
weaker if we carry another wire, in a somewhat larger arc,
around the part of the gutta-percha wire which projects beyond
the strips; the second wire cuts off from the first part of
the external eflect. Indeed, we may say that the edge of the
zinc strip itself in a similar way cuts off from the middle
of the strip some of the induction. For if we now remove
one of the two zinc strips and simply let the gutta-percha wire
rest upon the other, we always perceive sparks in the wire ;
but these are extremely feeble in the middle of the strip, and
much more powerful towards the edge. Just as electricity
when distributed by electrostatic induction would tend to
accumulate on the sharp edge of the strip, so here the current
seems by preference to move along the edge. In both cases
we may say that the outer parts protect the inner from an
influence exerted from the outside.

Equally convincing, and somewhat neater, are the follow-
ing experiments : — I inserted in the conductor, along which
the waves were transmitted, a very thick copper wire 1'5 metre
long, whose ends carried two circular metallic disks 15 cm.

X PROPAGATION OF ELECTRIC WAVES BY WIRES 165

in diameter. The wire passed through the centres of the disks
whose planes were perpendicular ,to it. Around the edge of
each disk were twenty-four equidistant holes. A spark-gap
was inserted in the wire. When the waves traversed the wire
they produced sparks up to 6 mm. in length. A thin copper
wire was now stretched across between two corresponding
holes in the disks. The sparking distance thereupon sank to
3*2 mm. No other change was produced when the thin wire
was replaced by a thick one, or when twenty-four wires were
used instead of the single one, provided they were drawn all
together through the same pair of holes. But it was other-
wise when the wires were distributed around the edge of the
disks. When a second wire was added opposite the first one
the spark-length sank to 1*2 mm. When two more wires
were put in midway between the others, the spark-length
went as low as 5 mm. The insertion of four more wires
in intermediate positions left sparks barely O'l mm. long ; and
after aU twenty-four wires were inserted at equal distances no
sparking whatever could be perceived inside. Yet the resistance
of the inner wire was much smaller than the joint resistance of
all the outer wires ; and furthermore, we have given a special
proof that the resistance is of no consequence. At the side of
the tube of wires which has been built up let us place as a
shunt a conductor precisely similar to the one inside the tube ;
we see vigorous sparking in the former, but none whatever in
the latter. The former is not screened, the latter is screened
by the tube of wires. We have here an electromagnetic
analogue to the electrostatic experiment known under the
name of the electric bird-cage.

Again I altered the experiment in the way indicated in
Fig. 33. The two disks were moved nearer together so that,

Cfc ^ //

Fig. 83,

with the wires stretched between them, they formed a wire-
cage A just big enough to contain the spark-micrometer. One
of the disks (a) remained in metallic connection with the
central wire ; the other (^) was insulated from it by cutting

166 PROPAGATION OF ELECTRIC WAVES BY WIRES x

out a round hole, and was instead connected with a conducting
tube 7 which, without touching the central wire, completely-
surrounded it for a distance of 1*5 metra The free end S of
the tube was then placed in metallic connection with the
central wire. The wire with its spark-gap still lies in a
space surrounded by a metallic screen ; and it seems to follow
naturally after what has already been stated that, whether
the waves be led through the arrangement in the one direction
or the other, not the slightest electrical disturbance would be
detected in the wire. So far, then, this arrangement offers
nothing new ; but it has this advantage over the preceding
one, that we can replace the protecting metal tube y by others
with thinner and thinner walls, and so find out what thickness
of wall is just sufficient to stop off the outside action. Very
thin brass tubes — tubes of tinfoil and tubes of Dutch metal —
acted as perfect screens. I next took glass tubes which had
been chemically silvered, and now found it quite easy to pre-
pare tubes so thin that, in spite of their protection, there was
vigorous sparking in the central wire. But the sparks only
appeared when the film of silver was so thin that it was no
longer quite opaque to light, and was certainly thinner than
TxAnx ™^- ^^ imagination, though not in practice, we may
draw the protecting envelope more and more closely around
the wire, until at last it coincides with its surface ; and we
may feel certain that nothing would practically be altered
thereby. So, however vigorously the waves may really play
about the wire, inside it is perfectly calm ; the action of the
waves scarcely penetrates further into the wire than does
the light which is reflected from its surface. Hence we
should expect to find the real seat of these waves in the
neighbourhood of the wire, and not in the wire itself; and
instead of saying that our waves are propagated in the
wire, we should rather say that they glide towards and along
the wire.

Instead of inserting the arrangement last described in the
conducting wire in which waves were indirectly produced, we
can insert it in one of the branches of the primary conductor
itself. In such experiments I obtained much the same results
as in the previous ones. Hence it must be equally true of
our primary oscillation, that its seat is not to be found in the

X PROPAGATION OF ELECTRIC WAVES BY WIRES 167

interior of the conductor ; only the outer skin of the con-
ductor, about which it plays, takes part in it.^

One further item of information may be added to what
we have already learned about waves in wires, and this relates
to the method of carrying out the experiments. If our waves
have their seat in the space surrounding the wire, then a wave
gliding along a single wire will not be propagated through the
air alone ; but, inasmuch as its action extends to a considerable
distance, it will be propagated in the neighbouring walls, the
floor, etc., and so will develop into a complicated phenomenon.
But if we set up in exactly the same way two auxiliary plates
opposite the two poles of our primary conductor, connect a
wire to each of them, and lead both wires straight and parallel
to one another to the same distance, then the action of the
waves makes itself felt only in the neighbourhood of the
space between the two wires. Hence it is only in the space
between the wires that the wave progresses. We can thus
take measures to secure that the propagation occurs only
through air or another insulator, and by so arranging matters
can experiment more conveniently and with less fear of com-
plications. The wave-lengths thus obtained are, however,
approximately the same as those obtained with single wires ;
so that even with the latter the disturbing efiects do not
seem to be of much importance.

3. From what has already been stated, we may conclude
that rapid electric oscillations are quite incapable of penetrating
metallic layers of any thickness, and that it is therefore quite
impossible to excite sparks by the aid of such oscillations
inside closed metallic envelopes. Hence, if we see sparks
induced by such oscillations inside metallic envelopes which
are nearly, but not quite, closed, we must conclude that the
electric disturbance has penetrated through the existing open-
ings. And this mode of conception is the correct one ; but
in some cases it contradicts the usual view so completely that
special experiments are required to induce us to forsake the
usual view for the newer one. We shall select a striking case
of this kind ; and by making certain of the correctness of our

^ The calcalation of the self-induction of such conductors on the assumption
of uniform current-density in the interior must therefore lead to totally un-
reliable results. It is surprising that the results obtained under such erroneous
assumptions should yet appear to agree approximately with the truth.

168 PROPAGATION OF ELECTRIC WAVES BY WIRES x

view in this case, we shall show its probability in all other
cases. We return to the arrangement described in the pre-
vious section, and represented in Fig. 33, only we no longer
connect the protecting tube at S with the central wire. We
now send the train of waves through the arrangement in the
direction from A towards S. We obtain brilliant sparks at -4,
and these are about as strong as if we had inserted the spark-
gap in the conducting wire without any protection. Nor do the
sparks become much smaller if, without altering anything else,
we lengthen the tube 7 considerably — up to about 4 metres.
According to the usual view, it would be said that the wave on
reaching A easily passes through the thin metal disk a, which
is a good conductor, then springs across the spark-gap at A and
proceeds along the central wire. According to our conception,
on the other hand, we ought to describe what happens as
follows : — The wave on reaching A is absolutely unable to pass
through the metal disk, so it glides along the disk over the
outside of the apparatus, travelling along thus until it reaches
the point S, 4 metres off. Here it divides — one part, which
at present does not concern us, immediately proceeds straight
along the wire ; another part bends round into the inside of
the tube and runs back the whole 4 metres in the air-space
between the tube and the central wire, until it reaches the
spark-gap Ay where it now produces sparks. We shall show
by the following experiments that our conception, although
somewhat complicated, is yet the correct one. In the first
place, every trace of sparking at A disappears as soon as we
close the opening at S, even if it be only with a tinfoil cap.
Our waves have a wave-length of only 3 metres ; before their
action has reached the point S, it has gone back to zero at -4,
and has changed sign. What influence then could the closing
of the distant opening at S exert upon the spaYk at A, if the
latter really appears as soon as the wave passes through the
metallic partition ? In the second place, the sparks disappear
when we make the central wire end inside the tube 7, or at
the open end S of this tube ; they reappear when the end of
the wire is allowed to project beyond the opening, even if only
for 20-30 cm. What influence could this insignificant length-
ening of the wire have upon the spark at -4, unless the pro-
jecting end of the wire were just the means by which a part

PKOPAGATION OF ELECTRIC WAVBCiAy'^iillttfii-'^^ 169

of the wave is intercepted and brought through the opening S
into the interior? Let us, in the third place, introduce a
second spark-gap jBin the central wire between A and S, and
surround it with a wire cage just like A, When we place the
poles in B so far apart that sparks can no longer pass, we find
that it is no longer possible to obtain any perceptible sparks
in A, But if, in like manner, we hinder the passage of the
sparks in -4, we find that this has scarcely any influence upon
the sparks in B. Hence, for the passage of the sparks in A,
it is requisite that they should first pass in B\ but for the
passage of sparks in jB, it is not necessary that they should
first pass in A, Hence the direction of propagation in the
interior is from B towards A, not from A towards B,

Moreover, we can adduce other and more convincing
proofs. By making the spark-gap either vanishingly smdll or
very great, we may prevent the wave returning from S towards
A from expending its energy in the formation of sparks. In
this case the wave will be reflected at -4, and will again pro-
ceed from A towards S. But in doing so it must combine
with the direct waves to form stationary oscillations with
nodes and antinodes. If we succeed in showing the presence
of these, we can no longer have any doubt as to the correct-
ness of our conception. For this purpose we must necessarily
give our apparatus somewhat different dimensions, so as to be
able to introduce electric resonators inside it. I therefore
carried the central wire through the axis of a cylindrical tube
5 metres long and 30 cm. in diameter. Tliis tube was not

Pig. 84.

made of solid metal, but was built up of twenty-four copper
wires ; these were stretched parallel to one another along the
generating surface over seven equidistant circular rings of
stout wire, as indicated in Fig. 34. The resonator to be used
I made as follows: — Copper wire 1 mm. thick was coiled
tightly into a spiral of 1 cm. diameter. About 125 turns of
this were taken, pulled out a little, and bent into a circle of
12 cm. diameter; between the free ends was inserted an

170 PROPAGATION OF ELECTRIC WAVES BY WIRES x

adjustable spark-gap. Special experiments had shown that
this circle was in resonance with the waves of 3 metres length
in the wire, and yet it was suflSciently small to be introduced
between the central wire and the tube. Both ends of the
tube were at first left open, and the resonator was held inside
in such a way that its plane included the central wire, and
the spark-gap was not turned exactly inwards or outwards,
but faced towards one or other end of the tube; vigorous
sparks, ^-I mm. long, appeared at the spark-gap. If now
both ends of the tube were closed by four wires arranged
crosswise and connected with the central conductor, not the
slightest sparking could be discovered inside, which proves
that the network of the tube is sufficiently close for our ex-
periments. In the next place, the cross-wires on the )8 side
of the tube (i,e, the side remote from the origin of the waves)
were removed. No sparks could be detected when the resonator
was in the immediate neighbourhood of the remaining cross-
wires, i.e. in the position a, which corresponds to the spark-gap A
of our earlier experiments. But when it was moved from this
position towards )8 the sparks reappeared, became very vigorous
at a distance of 1*5 metre from a, decreased again and almost
completely disappeared at a distance of 3 metres, and again
became stronger towards the end of the tube. Our supposition
is therefore confirmed. It is right that there should be a node
at the closed end, for at the metallic connection between the
central wire and the tube the electric force between both must
necessarily be zero. It is otherwise if we cut the central
conductor at this point, quite near the cross-wires, leaving a
gap a few centimetres long. In this case the wave is reflected
with the opposite phase, and we should expect an antinode at
a. And, in fact, we do now find vigorous sparks in the reson-
ator ; these, however, rapidly become smaller as we move from
a towards fi, disappear almost entirely at a distance of 1*5
metre, become vigorous again at a distance of 3 metres, and
finally give plain indications of a second node at a distance of
4'5 metres, i.e. 0*5 metre from the open end of the tube.
The nodes and antinodes which we have described lie at fixed
distances from the closed end, and alter their position as this
does ; but otherwise they are quite independent of processes
going on outside the tube, e.g. of the nodes and antinodes which

X PROPAGATION OF ELECTRIC WAVES BY WIRES 171

we may produce there. The phenomena occur in precisely the
same way when we allow the waves to traverse the tube in the
opposite direction, i.e. from the open to the closed end ; but this
case is less interesting, because the mode of propagation of the
waves here differs less from the usual conception than in the
case which we have just discussed. If we leave the central
wire uncut, and both ends of the tube open, and produce in
the whole system stationary waves, with nodes and autinodes,
we always find a node inside the tube corresponding to each
node outside, which proves that the rate of propagation is
approximately the same inside and outside.

On studying the experiments above described, the mode
in which we have interpreted them, and the explanations of
the investigators referred to in the introduction, one differ-
ence will be found especially striking between the con-
ception here advocated and the usually accepted view. In
the latter conductors appear as the only bodies which take
part in the propagation of electrical disturbances — non-con-
ductors as bodies which oppose this propagation. According
to our conception, on the other hand, all propagation of
electrical disturbances takes place through non-conductors ;
and conductors oppose this propagation with a resistance
which, in the case of rapid alternations, is insuperable. We
might almost feel inclined to agree to the statement that
conductors and non-conductors should, according to this con-
ception, have their names interchanged. Such a paradox,
however, only arises because we omit to specify what conduc-
tion or non- conduction is under discussion. Undoubtedly
metals are non-conductors for electric force, and for this very
reason they, under certain conditions, restrain it from becoming
dissipated, and compel it to remain concentrated ; they thus
become conductors of the apparent source of these forces —
the electricity — to which the usual terminology has reference.

XI
ON ELECTRIC RADIATION

{SUzttngsber. d. Berl. Akad. d. Wiss. Dec. 13, 1888. Wiedem/inrCs Ann.

36, p. 769.)

As soon as I had succeeded in proving that the action of an
electric oscillation spreads out as a wave into space, I planned
experiments with the object of concentrating this action and
making it perceptible at greater distances by putting the
primary conductor in the focal line of a large concave
parabolic mirror. These experiments did not lead to the
desired result, and I felt certain that the want of success was
a necessary consequence of the disproportion between the
length (4-5 metres) of the waves used and the dimensions
which I was able, under the most favourable circumstances, to
give to the mirror. Recently I have observed that the
experiments which I have described can be carried out quite
well with oscillations of more than ten times the frequency,
and with waves less than one-tenth the length of those which
were first discovered. I have, therefore, returned to the use of
concave mirrors, and have obtained better results than I had
ventured to hope for. I have succeeded in producing distinct
rays of electric force, and in carrying out with them the
elementary experiments which are commonly performed with
light and radiant heat. The following is an account of these
experiments : —

The Apparatus

The short waves were excited by the same method which
we used for producing the longer waves. The primary

XI ELECTRIC RADIATION 173

conductor used may be most simply described as follows : —
Imagine a cylindrical breiss body/ 3 cm. in diameter and
26 cm. long, interrupted midway along its length by a spark-
gap whose poles on either side are formed by spheres of 2 cm.
radius. The leugth of the conductor is approximately equal
to the half wave-length of the corresponding oscillation in
straight wires ; from this we are at once able to estimate
approximately the period of oscillation. It is essential that
the pole -surfaces of the spark-gap should be frequently
repolished, and also that during the experiments they should
be carefully protected from illumination by simultaneous side-
discharges ; otherwise the oscillations are not excited. Whether
the spark-gap is in a satisfactory state can always be recognised
by the appearance and sound of the sparks. The discharge is
led to the two halves of the conductor by means of two gutta-
percha-covered wires which are connected near the spark-gap
on either side. I no longer made use of the large Euhmkorff,
but found it better to use a small induction-coil by Keiser and
Schmidt; the longest sparks, between points, given by this
were 4*5 cm. long. It was supplied with current from three
accumulators, and gave sparks 1-2 cm. long between the
spherical knobs of the primary conductor. For the purpose
of the experiments the spark-gap was reduced to 3 mm.

Here, again, the small sparks induced in a secondary
conductor were the means used for detecting the electric forces
in space. As before, I used partly a circle which could be
rotated within itself and which had about the same period of
oscillation as the primary conductor. It was made of copper
wire 1 mm. thick, and had in the present instance a diameter
of only 7*5 cm. One end of the wire carried a polished brass
sphere a few millimetres in diameter ; the other end was
pointed and could be brought up, by means of a fine screw
insulated from the wire, to within an exceedingly short
distance from the brass sphere. As will be readily under-
stood, we have here to deal only with minute sparks of a few
hundredths of a millimetre in length ; and after a little practice
one judges more according to the brilliancy than the length of
the sparks.

The circular conductor gives only a differential effect, and

* See Figs. 35 and 36 and the description of them at the end of this paper.

174 ^ ELECTRIC RADIATION xi

is not adapted for use in the focal line of a concave mirror.
Most of the work was therefore done with another conductor
arranged as follows : — Two straight pieces of wire, each 50 cm.
long and 5 mm. in diameter, were adjusted in a straight line
so that their near ends were 5 cm. apait. From these ends
two wires, 15 cm. long and 1 mm. in diameter, were carried
parallel to one another and perpendicular to the wires first
mentioned to a spark-gap arranged just as in the circular
conductor. In this conductor the resonance-action was given
up, and indeed it only comes slightly into play in this case. It
would have been simpler to put the spark-gap directly in the
middle of the straight wire ; but the observer could not then
have handled and observed the spark-gap in the focus of the
mirror without obstructing the apertura For this reason the
arrangement above described was chosen in preference to the
other which would in itself have been more advantageous.

The Production of the Ray

If the primary oscillator is now set up in a fairly large
free space, one can, with the aid of the circular conductor,
detect in its neighbourhood on a smaller scale all those
phenomena which I have already observed and described as
occurring in the neighbourhood of a larger oscillation.^ The
greatest distance at which sparks could be perceived in the
secondary conductor was 1*5 metre, or, when the primary spark-
gap was in very good order, as much as 2 metres. When a plane
reflecting plate is set up at a suitable distance on one side of the
primary oscillator, and parallel to it, the action on the opposite
side is strengthened. To be more precise : — If the distance
chosen is either very small, or somewhat greater than 30 cm.,
the plate weakens the effect ; it strengthens the effect greatly
at distances of 8-15 cm., slightly at a distance of 45 cm., and
exerts no influence at greater distances. We have drawn
attention to this phenomenon in an earlier paper, and we
conclude from it that the wave in air corresponding to the
primary oscillation has a half wave-length of about 30 cm. We
may expect to find a still further reinforcement if we replace
the plane surface by a concave mirror having the form of a

1 See v., VII., VIII.

XI ELECTKIC RADIATION 175

parabolic cylinder, in the focal line of which the axis of the
primary oscillation lies. The focal length of the mirror
should be chosen as small as possible, if it is properly to
concentrate the action. But if the direct wave ia not
to annul immediately the action of the reflected wave, the
focal length must not be much smaller than a quarter wave-
length. I therefore fixed on 12^ cm. as the focal length, and
constructed the mirror by bending a zinc sheet 2 metres long,
2 metres broad, and ^ mm. thick into the desired shape over a
wooden frame of the exact curvature. The height of the
mirror was thus 2 metres, the breadth of its aperture 1*2
metre, and its depth 0*7 metre. The primary oscillator was
fixed in the middle of the focal line. The wires which
conducted the discharge were led through the mirror; the
induction-coil and the cells were accordingly placed behind
the mirror so as to be out of the way. If we now investigate
the neighbourhood of the oscillator with our conductors, we
find that there is no action behind the mirror or at either side
of it ; but in the direction of the optical axis of the mirror the
sparks can be perceived up to a distance of 5-6 metres. When
a plane conducting surface was set up so as to oppose the
advancing waves at right angles, the sparks could be detected
in its neighbourhood at even greater distances — up to about
9-10 metres. The waves reflected from the conducting surface
reinforce the advancing waves at certain points. At other
points again the two sets of waves weaken one another. In
front of the plane wall one can recognise with the rectilinear con-
ductor very distinct maxima and minima, and with the circular
conductor the characteristic interference-phenomena of stationary
waves which I have described in an earlier paper. I was able
to distinguish four nodal points, which were situated at the
wall and at 33, 65, and 98 cm. distance from it. We thus get
33 cm. as a closer approximation to the half wave-length of the
waves used, and 1*1 thousand-millionth of a second as their
period of oscillation, assuming that they travel with the
velocity of light. In wires the oscillation gave a wave-length
of 29 cm. Hence it appears that these short waves also have
a somewhat lower velocity in wires than in air ; but the ratio
of the two velocities comes very near to the theoretical value
— unity — and does not differ from it so much as appeared to

176 ELECTRIC RADIATION xi

be probable from our experiments on longer waves. This
remarkable phenomenon still needs elucidation. Inasmuch as
the phenomena are only exhibited in the neighbourhood of the
optic axis of the mirror, we may speak of the result produced
as an electric ray proceeding from the concave mirror.

I now constructed a second mirror, exactly similar to the
first, and attached the rectilinear secondary conductor to it in
such a way that the two wires of 50 cm. length lay in the
focal line, and the two wires connected to the spark-gap passed
directly through the walls of the mirror without touching it.
The spark-gap was thus situated directly behind the mirror,
and the observer could adjust and examine it without obstruct-
ing the course of the waves. I expected to find that, on inter-
cepting the ray with this apparatus, I should be able to observe
it at even greater distances ; and the event proved that I was
not mistaken. In the rooms at my disposal I could now
perceive the sparks from one end to the other. The greatest
distance to which I was able, by availing myself of a doorway,
to follow the ray was 16 metres ; but according to the results
of the reflection-experiments (to be presently described), there
can be no doubt that sparks could be obtained at any rate up
to 20 metres in open spaces. For the remaining experiments
such great distances are not necessary, and it is convenient
that the sparking in the secondary conductor should not be too
feeble; for most of the experiments a distance of 6-10 metres
is most suitable. We shall now describe the simple pheno-
mena which can be exhibited with the ray without difficulty.
When the contrary is not expressly stated, it is to be assumed
that the focal lines of both mirrors are vertical.

Rectilinear Propagation

If a screen of sheet zinc 2 metres high and 1 metre broad
is placed on the straight line joining both mirrors, and at right
angles to the direction of the ray, the secondary sparks dis-
appear completely. An equally complete shadow is thrown by
a screen of tinfoil or gold-paper. If an assistant walks across
the path of the ray, the secondary spark-gap becomes dark as
soon as he intercepts the ray, and again lights up when he
leaves the path clear. Insulators do not stop the ray — it

XI ELECTRIC RADIATION 177

passes right through a wooden partition or door ; and it is not
without astonishment that one sees the sparks appear inside a
closed room. If two conducting screens, 2 metres high and 1
metre broad, are set up symmetrically on the right and left of the
ray, and perpendicular to it, they do not interfere at all with
the secondary spark so long as the width of the opening between
them is not less than the aperture of the mirrors, viz. 1*2 metre.
If the opening is made narrower the sparks become weaker,
and disappear when the width of the opening is reduced below
0*5 metre. The sparks also disappear if the opening is left
with a breadth of 1*2 metre, but is shifted to one side of the
straight line joining the mirrors. If the optical axis of the
mirror containing the oscillator is rotated to the right or left
about 10° out of .the proper position, the secondary sparks
become weak, and a rotation through 15° causes them to
disappear.

There is no sharp geometrical limit to either the ray or the
shadows; it is easy to produce phenomena corresponding to
diffraction.^ As yet, however, I have not succeeded in
observing maxima and minima at the edge of the shadows.

Polarisation

From the mode in which our ray was produced we can
have no doubt whatever that it consists of transverse vibrations
and is plane-polarised in the optical sense. We can also prove
by experiment that this is the case. If the receiving mirror
be rotated about the ray as axis until its focal line, and there-
fore the secondary conductor also, lies in a horizontal plane,
the secondary sparks become more and more feeble, and when
the two focal lines are at right angles, no sparks whatever are
obtained even if the mirrors are moved close up to one another.
The two mirrors behave like the polariser and analyser of a
polarisation apparatus.

I next had made an octagonal frame, 2 metres high and
2 metres broad ; across this were stretched copper wires 1 mm.
thick, the wires being parallel to each other and 3 cm. apart.
If the two mirrors were now set up with their focal lines
parallel, and the wire screen was interposed perpendicularly to

^ [See Note 25 at end of book.]

178 ELECTRIC RADIATION xi

the ray and so that the direction of the wires wa$ perpendicular
to the direction of the focal lines, the screen practically did not
interfere at all with the secondary sparks. But if the screen
was set up in such a way that its wires were parallel to the
focal lines, it stopped the ray completely. With regard, then,
to transmitted energy the screen behaves towards our ray just
as a tourmaline plate behaves towards a plane-polarised ray of
light. The receiving mirror was now placed once more so that
its focal line was horizontal; imder these circumstances, as
already mentioned, no sparks appeared. Nor were any sparks
produced when the screen was interposed in the path of the
ray, so long as the wires in the screen were either horizontal
or vertical. But if the frame was set up in such a position
that the wires were inclined at 45° to the horizontal on either
side, then the interposition of the screen immediately produced
sparks in the secondary spark-gap. Clearly the screen resolves
the advancing oscillation into two components and transmits
only that component which is perpendicular to the direction
of its wires. This component is inclined at 45° to the focal
line of the second mirror, and may thus, after being again
resolved by the mirror, act upon the secondary conductor. The
phenomenon is exactly analogous to the brightening of the dark
field of two crossed Nicols by the interposition of a crystalline
plate in a suitable position.

With regard to the polarisation it may be further observed
that, with the means employed in the present investigation,
we are only able to recognise the electric force. When the
primary oscillator is in a vertical position the oscillations of
this force undoubtedly take place in the vertical plane through
the ray, and are absent in the horizontal plane. But the results
of experiments with slowly alternating currents leave no room
for doubt that the electric oscillations are accompanied by
oscillations of magnetic force which take place in the horizontal
plane through the ray and are zero in the vertical plane. Hence
the polarisation of the ray does not so much consist in the
occurrence of oscillations in the vertical plane, but rather in the
fact that the oscillations in the vertical plane are of an electrical
nature, while those in the horizontal plane are of a magnetic
nature. Obviously, then, the question, in which of the two
planes the oscillation in our ray occurs, cannot be answered

XI ELECTRIC RADIATION 179

unless one specifies whether the question relates to the electric
or the magnetic oscillation. It was Herr Kolacek ^ who first
pointed out clearly that this consideration is the reason why
an old optical dispute has never been decided.

Reflection

We have already proved the reflection of the waves from
conducting surfaces by the interference between the reflected
and the advancing waves, and have also made use of the
reflection in the construction of our concave mirrors. But now
we are able to go further and to separate the two systems of
waves from one another. I first placed both mirrors in a large
room side by side, with their apertures facing in the same
direction, and their axes converging to a point about 3 metres
off. The spark-gap of the receiving mirror naturally remained
dark. I next set up a plane vertical wall made of thin sheet
zinc, 2 metres high and 2 metres broad, at the point of inter-
section of the axes, and adjusted it so that it was equally
inclined to both. I obtained a vigorous stream of sparks
arising from the reflection of the ray by the walL The
sparking ceased as soon as the wall was rotated around a
vertical axis through about 15° on either side of the correct
position ; from this it follows that the reflection is regular, not
diffuse. When the wall was moved away from the mirrors, the
axes of the latter being still kept converging towards the wall,
the sparking diminished very slowly. I could still recognise
sparks when the wall was 10 metres away from the mirrors,
i.e, when the waves had to traverse a distance of 20 metres.
This arrangement might be adopted with advantage for the
purpose of comparing the rate of propagation through air with
other and slower rates of propagation, e.g. through cables.

In order to produce reflection of the ray at angles of
incidence greater than zero, I allowed the ray to pass parallel
to the wall of the room in which there was a doorway. In
the neighbouring room to which this door led I set up the
receiving mirror so that its optic axis passed centrally through
the door and intersected the direction of the ray at right angles.
If the plane conducting surface was now set up vertically at

1 [F. Koladek, Wied. Ann, 34, p. 676, 1888.]

180 ELECTBIC RADIATION xi

the point of intersection, and adjusted so as to make angles of
45° with the ray and also with the axis of the receiving mirror,
there appeared in the secondary conductor a stream of sparks
which was not interrupted by closing the door. When I turned
the reflecting surface about 10° out of the correct position the
sparks disappeared. Thus the reflection is regular, and the
angles of incidence and reflection are equal. That the action
proceeded from the source of disturbance to the plane mirror,
and hence to the secondary conductor, could also be shown by
placing shadow-giving screens at diflferent points of this path.
The secondary sparks then always ceased immediately ; whereas
no effect was produced when the screen was placed anywhere
else in the room. With the aid of the circular secondary con-
ductor it is possible to determine the position of the wave-front
in the ray ; this was found to be at right angles to the ray
before and after reflection, so that in the reflection it was turned
through 90°.

Hitherto the focal hues of the concave mirrors were vertical,
and the plane of oscillation was therefore perpendicular to the
plane of incidence. In order to produce reflection with the
oscillations in the plane of incidence, I placed both mirrors with
their focal lines horizontal. I observed the same phenomena
as in the previous position ; and, moreover, I was not able to
recognise any diflference in the intensity of the reflected ray in
the two cases. On the other hand, if the focal line of the one
mirror is vertical, and of the other horizontal, no secondary
sparks can be observed. The inclination of the plane of oscilla-
tion to the plane of incidence is therefore not altered by re-
flection, provided this inclination has one of the two special
values referred to ; but in general this statement cannot
hold good. It is even questionable whether the ray after
reflection continues to be plane-polarised. The interferences
which are produced in front of the mirror by the intersecting
wave-systems, and which, as I have remarked, give rise to
characteristic phenomena in the circular conductor, are most
likely to throw light upon all problems relating to the change
of phase and amphtude produced by reflection.

One further experiment on reflection from an electrically
eolotropic surface may be mentioned. The two concave mirrors
were again placed side by side, as in the reflection-experiment

XI ELECTRIC RADIATION 181

first described ; but now there was placed opposite to them, as
a reflecting surface, the screen of parallel copper wires which
has already been referred to. It was found that the secondary
spark-gap remained dark when the wires intersected the direction
of the oscillations at right angles, but that sparking began as
soon as the wires coincided with the direction of the oscillations.
Hence the analogy between the tourmaline plate and our surface
which conducts in one direction is confined to the transmitted
part of the ray.^ The tourmaline plate absorbs the part which
is not transmitted ; our surface reflects it. If in the experiment
last described the two mirrors are placed with their focal lines at
right angles, no sparks can be excited in the secondary conductor
by reflection from an isotropic screen; but I proved to my
satisfaction that sparks are produced when the reflection takes
place from the eolotropic wire grating, provided this is adjusted
so that the wires are inclined at 45° to the focal lines. The
explanation of this follows naturally from what has been already
stated.

Refraction

In order to find out whether any refraction of the ray takes
place in passing from air into another insulating medium, I had
a large prism made of so-called hard pitch, a material like
asphalt. The base was an isosceles triangle 1*2 metres in the
side, and with a refracting angle of nearly 30°. The refracting
edge was placed vertical, and the height of the whole prism was
1*5 metres. But since the prism weighed about 12 cwt., and
would have been too heavy to move as a whole, it was built up
of three pieces, each 0*5 metre high, placed one above the other.
The material was cast in wooden boxes which were left around
it, as they did not appear to interfere with its use. The prism
was mounted on a support of such height that the middle of
its refracting edge was at the same height as the primary and
secondary spark-gaps. When I was satisfied that refraction
did take place, and had obtained some idea of its amount, I
arranged the experiment in the following manner ; — The produc-
ing mirror was set up at a distance of 2*6 metres from the
prism and facing one of the refracting surfaces, so that the axis
of the beam was directed as nearly as possible towards the centre

1 [See Note 26 at end of book.]

182 ELECTRIC RADIATION xi

of mass of the prism, and met the refiracting surface at an
angle of incidence of 25^ (on the side of the normal
towards the base). Near the refracting edge and also at the
opposite side of the prism were placed two conducting screens
which prevented the ray from passing by any other path than
that through the prism* On the side of the emerging ray there
was marked upon the floor a circle of 2*5 metres radius, having
as its centre the centre of mass of the lower end of the prism.
Along this the receiving mirror was now moved about, its aper-
ture being always directed towards the centre of the circle.
No sparks were obtained when the mirror was placed in the
direction of the incident ray produced ; in this direction the
prism threw a complete shadow. But sparks appeared when
the mirror was moved towards the base of the prism, beginning
when the angular deviation from the first position was about
11° The sparking increased in intensity until the deviation
amounted to about 22°, and then again decreased. The last
sparks were observed with a deviation of about 34°. When
the mirror was placed in a position of maximum effect, and then
moved away from the prism along the radius of the circle, the
sparks could be traced up to a distance of 5-6 metres.
When an assistant stood either in front of the prism or behind
it the sparking invariably ceased, which shows that the action
reaches the secondary conductor through the prism and not in
any other way. The experiments were repeated after placing
both mirrors with their focal lines horizontal, but without alter-
ing the position of the prism. This made no difference in the
phenomena observed. A refracting angle of 30° and a devia-
tion of 22° in the neighbourhood of the minimum deviation
corresponds to a refractive index of 1*69. The refractive index
of pitch-like materials for light is given as being between 1*5
and 1"6. We must not attribute any importance to the
magnitude or even the sense of this difference,^ seeing that our
method was not an accurate one, and that the material used
was impure.

We have applied the term rays of electric force to the
phenomena which we have investigated. We may perhaps
further designate them as rays of light of very great wave-length.
The experiments described appear to me, at any rate, eminently

* [See Note 27 at end of book.]

XI ELECTRIC RADIATION 183

adapted to remove any doubt ae to the identity of light, radiant
heat, and electromagnetic wave-motion. I believe that from
now on we shall have greater confidence in making use of the
advantages which this identity enables us to derive both in the
study of optics and of electricity.

Sai^analion. of the Fibres. — In order to facilitate the
repetition and extension of these experiments, I append in
the accompanying Figs. 35,
36^ and 36t,, illustrations of
the apparatus which I used,
although these were constructed
simply for the purpose of experi-
menting at the time and with-
out any regard to durability.
Fig. 35 shows in plan and ele-
vation (section) the producing
mirror. It will be seen that
the framework of it consists of
two horizontal frames (a, a) of
parabolic form, and four vertical
supports (ft, 6)which are screwed
to each of the frames so a.1 to
support and connect them. The
sheet metal reflector is clamped
between the frames and the sup-
ports, and fastened to both by
numerous screws. The sup-
ports project above and below
beyond the sheet metal so Kg. 35.

that they can be used as

handles in handling the mirror. Fig. 36, represents the
primary conductor on a somewhat larger scale. The two metal
parts slide with friction in two sleeves of strong paper which
are held together by indiarubber bands. The sleeves them-
selves are fastened hy four rods of sealing-wax to a board which
again is tied by indiarubber hands to a strip of wood forming
part of the frame which can be seen in Fig. 35. The two leading

184

ELECTRIC RADIATION

wires (covered with gutta-percha) terminate in two holes bored
in the knobe of the primary conductor. This arrangement
allows of all necessary motioD and adjustment of the various
parts of the conductor ; it can be taken to pieces and put
together again in a few minutes, and this is essential in oi^er
that the knobs may be frequently repolished. Just at the
points where the leading wires pass through the mirror, they

are surrounded duiing the diachai^e by a hloish light. The
smooth wooden screen s is introduced for the purpose of shield-
ing the spark-gap from this light, which otherwise would
interfere seriously with the production of the oscillations.
Lastly, rig. 3 6^ represents the secondary spark-gap. Both parts
of the secondary conductor are again attached by sealing-wax
rods and indiarubber bands to a slip forming part of the wooden
framework. From the inner ends of these parts the leading
wires, surrounded by glass tubes, can be seen proceeding through
the mirror and bending towards one another. The upper wire
carries at its pole a smaU brass knob. To the lower wire is
soldered a piece of watch-spring which carries the second pole,
consisting of a fine copper point. The point is intentionally
chosen of softer metal than the knob ; unless this precaution is
taken the point easily penetrates into the knob, and the minute
sparks disappear from sight in the small hole thus produced.
The figure shows how the point is adjusted by a screw which
presses against the spring that is insulated from it by a glass
plate. The spring is bent in a particular way in order to secure

XI ELECTRIC RADIATION 185

finer motion of the point than would be possible if the screw
alone were used.

No doubt the apparatus here described can be considerably
modified without interfering with the success of the experi-
ments. Acting upon friendly advice, I have tried to replace
the spark-gap in the secondary conductor by a frog's leg pre-
pared for detecting currents ; but this arrangement which is so
delicate under other conditions does not seem to be adapted for
these purposes.^

^ [See Note 28 at end of book. ]

XII

ON THE MECHANICAL ACTION OP ELECTRIC WAVES

IN WIRES

(Wiedemann's Ann. 42, p. 407, 1891.)

The investigation of the mechanical forces to which a con-
ductor is subjected under the action of a series of electric
waves appeared to me to be desirable for several reasons. In
the first place, these forces might supply a means of investi-
gating such waves quantitatively, provided that the effects
observed were of sufi&cient magnitude and regularity. Hitherto
almost the only quantitative determinations have been based
on the heating effect of the waves. In the hands of Herren
Rubens and Ritter this method has given excellent results ; ^
but the observation of the mechanical forces offers in many
cases the advantage of simplicity. In the second place, by
examining the nature and distribution of the mechanical forces,
I hoped to find a means of demonstrating the existence of the
magnetic force in addition to the electric force. Only the
latter has manifested itself in the observations hitherto made ; ^
and as the ordinary methods of detecting magnetic force are of
no avail here, it appeared to be worth while trying whether a
new method would prove more serviceable. In the third and
last place — and this was more especially the object of the in-
vestigation — I hoped to be able to devise some way of making
observations on waves in free air, — that is to say, in such a
manner that any disturbances which might be observed could

^ H. Rubens and R. Ritter, TFied, Ann. 40, p. 56, 1890.

^ If I have myself on former occasions happened to speak of the observation
of nodes of the magnetic waves, this mode of expression was only justified by
theory and not required by experiment.

XII MECHANICAL ACTION OF ELECTRIC WAVES IN WIRES 187

in no wise be referred to any action-at-a-distance. This last
hope was frustrated by the feebleness of the effects produced
under the circumstances. I had to content myself with
examining the effects produced by waves travelling along
wires, although in so doing the most important object of the
experiments was missed. The mechanical actions produced by
waves in wires may be and will be regarded as being due to
attractions caused by the electrification of the wires and by
the currents flowing in them. For this reason researches on
waves in wires cannot be made use of to decide between the
older and the newer views. If, however, we start from the
point of view from which waves in wires are regarded simply
as a special form of waves travelling in air, it is a matter of
indifference whether we make the one form or the other the
object of our experiments.

1. The System of Waves Employed

After trying several ways of disposing the waves, and
after obtaining results which in the main were concordant, I
decided to adhere to Herr Lecher's arrangement as being the
neatest and the most suitable for the investigation.^ Fig. 37
shows the form thereof.

Fig. 87.

A A' is the same conductor which was always used before
as the primary conductor, and consists of two square plates,
each 40 cm. in the side, connected by a wire 60 cm. long
which contains a 2 mm. spark-gap. A small induction-coil
was used as an exciter ; this was supplied with current from
two accumulators, and its maximum spark-length was only 4
cm. Single discharges of this smaller apparatus were certainly
less efficient than those of a larger induction-coil, but this

1 E. Lecher, Wied, Ann. 41, p. 850, 1890.

188 MECHANICAL ACTION OF ELECTRIC WAVES IN WIRES xii

drawback was more than compensated for by the more rapid
succession of discharges. Opposite the plates A and A\ and
at a distance of 10 cm. from them, stood the plates B and B^^
from which two parallel wires, about 30 cm. apart, are led to
a distance of 6*8 metres, and there are connected together
between h and If. At a variable distance a a' from their
origin these wires are placed in communication with each
other by means of a second connection or bridge. When this
bridge is in a certain position, at a distance of about 1*2 metre
from Bff, there takes place in the interval between aa' and hJ/
a very energetic oscillation. This indicates the half wave-
length of a stationary wave, and, as Herr Lecher has shown, it
is produced by resonance between this oscillation itself and
the primary oscillation, which here takes place in the interval
between A A' on the one hand, and Ba a!B/ on the other hand.
Any shifting of the bridge increases one of the two periods of
oscillation, and at the same time diminishes the other ; hence
the peculiar definiteness of adjustment with this arrangement.
Besides its general excellence it offers for our present purpose
several special advantages. Since the forces to be observed
are very small, we have to protect carefully the conductors
which are subjected to them from external electrostatic effects.
With the arrangement here used this is possible, because the
wires, which we must necessarily place near the test-body,
form a connected conducting system. If in our experiments
we surround the working parts (of the apparatus) with a wire
network, and connect this with the nodal points at ad and &&',
the protection is made complete without interfering with
the vibration. Hence the experiments are carried out in this
way. Again, since the conductors which are to be subjected
to the forces do not, like the resonators previously used, pick
out a definite vibration from the whole disturbance, we could
only expect confused results if we did not otherwise take care
to produce a simple oscillation of definite wave-length and with
nodes in known positions. This condition is fulfilled in the
above arrangement ; for there can be no doubt that the points
aoi and hV are nodal points of all oscillations excited between
them, and that among these only the longest oscillation,
strengthened by resonance, rises to a considerable magnitude.
Clearly, we do not narrow the scope of the experiments by

XII

MECHANICAL ACTION OF ELECTRIC WAVES IN WIRES

189

contenting ourselves with the investigation of half a wave-
length. Finally, the conditions of our oscillation are practically
the same whether the two wires are stretched straight, or
whether they are bent side by side in any desired way ; just
as, in the case of acoustic vibrations of air in tubes, it is not
of much importance whether the tubes are straight or crooked.
We can thus easily bring our oscillation into all possible
positions with respect to the test-body which is held in a fixed
position. As a matter of fact, the various relative positions were
always obtained by shifting the wire, even in cases in which it
may appear from the text that the test-body had been shifted.

2. The Electric Force

For the purpose of measuring the mechanical action of the
electric force, I made use of a small cylindrical tube of gold
paper 5*5 cm. long, and 0*7 cm. in diameter. This was sus-
pended by a silk fibre with its
axis horizontal; a very small
magnet gave the tube a definite
position of rest, and a deviation
from this position was measured
by means of a small mirror. The
whole system hung in a glass
case, as shown in Fig. 38.
When the apparatus was sub-
jected to the action of the oscil-
lation, the needle tended to set
along the mean direction of the
electric force, and was thus de-
flected from the position of rest.
In order to increase these de-
flections I brought the two wires
in the neighbourhood of the ap-
paratus nearer to one another and
to the test-body — ^in fact, within
a few centimetres; and in order
to strengthen the action I at-
tached small plates to the wires opposite to the ends of the
test-body, as shown for one special case in the figure. Under

Fig. 88.

190 MECHANICAL ACTION OF ELECTRIC WAVES IN WIRES Xli

these circumstances first deflections of 100 scale divisions
and above could be obtained. These first throws exhibited a
satisfactory regularity ; when the same experiment was repeated
several times, the separate results only differed from one
another by a few per cent. The differences between single
discharges ought to be much greater, but the throw of the
needle gives the mean effect of very many discharges. In
order to show how these throws can be used in quantitative
experiments I here quote two series of observations. The
first of these is intended to illustrate the effect of resonance.
The apparatus was set up at c at the antinode of an oscillation,
and the wires ab and a'&' were brought near to it, as shown in
Fig. 38. The bridge aa^ was now placed at various distances
e from the origin £^ of the wires, the induction-apparatus was
put into action, and the magnitude i of the throw measured.
The respective values of e and i in the neighbourhood of the
maximum were : —

e = 80 90 100 110 120 130 140 150 160 cm.
i= 5-3 10-0 21-8 51-2 44-1 19-3 10*3 5*7 4*2 div.

When the throws are represented graphically it is seen
that their course is regular and exhibits a pronounced maximum
between 110 and 120 cm. In fact, the throws reach their
largest value i=60*6 scale divisions at e=114 cm.

The second series of observations was intended to exhibit
the decrease in the intensity of the oscillation from the antinode
c to the node i. For this purpose the distance was divided
into 12 equal divisions, and the apparatus was introduced at the
13 end-points. The following first throws i were obtained: —

1 2 3 4 5 6 7 8 9 10 11 12 13
80-5 80-5 79-0 77-0 65'6 578 50*0 38*5 275 17*5 70 1-0

These values again give a sufficiently smooth curve and
enable us to form an idea of the nature of the oscillation, and
to convince ourselves that it differs appreciably from the
simple sine-oscillation.

Other experiments which I planned had reference to the
direction of the electric force in the neighbourhood of the
wires. These experiments gave no fresh information beyond

XII

MECHANICAL ACTION OF ELECTRIC WAVES IN WIRES

191

what might be regarded as already settled. In the interval
between the wires the needle tended to set along the shortest
line between the two wires ; outside this space it tended to
take up the direction towards the nearest wire. Thus there was
always an apparent attraction to be observed between the ends
of the tube and the nearest parts of the wires.

3. The Magnetic Force

In order to investigate the magnetic force I made use of a
circular hoop of aluminium wire. The diameter of this hoop
was 65 mm., and that of the wire was 2 mm. The hoop was
suspended so that it could turn about a vertical diameter, and,
like the cylinder in the last section, was provided with a
magnet, mirror, and glass case.
Fig. 39 gives a sketch of the
apparatus used.

If we disregard for a moment
our knowledge of the magnetic
force we should expect that,
under the influence of the oscilla-
tion, the hoop would behave just
like the cylinder, and therefore
that the direction of the parts
which are farthest from the axis
of rotation, i.e, that the horizontal
diameter of the hoop would play
the same part as the axis of
length of the cylinder. We
should therefore expect the end-
points of the horizontal diameter
would everywhere be attracted by
the nearest parts of the wires
through which the waves are pass- '
ing, and that this action would be
strongest at the antinode of the

oscillation, and would cease in the neighbourhood of the nodes
where the electric force itself disappears. But if we actually
hang up the hoop at the node h 6', in the manner shown in Fig.
39, we observe other and unexpected phenomena. In the

Fig. 89.

192 MECHANICAL ACnOK OF ELECTRIC WAVES IK WIRES xii

first place, the ring does not remain at rest under the influence
of the oscillation, but exhibits deflections of the same order of
magnitude as those shown by the cylinder at the antinode of
the oscillation. In the second place, the deflection does ' not
indicate an attraction but a repulsion between the neighbouring
points of the hoop and the wires. That the repulsion is a
consequence of the oscillation itself is shown by the fact that
its magnitude is found to' be determined by resonance, accord-
ing to the same law as that of the electrical action. If we
leave the hoop inside the bent wire b b\ but alter the relative
positions of the two, we find that the horizontal diameter
always, and from all sides, endeavours to take up a position
perpendicular to the plane of the bent wire.

After these experiments alone, and apart from any knowledge
obtained otherwise, we may therefore assert that, in addition to
the electric oscillation, there is present an oscillation of another
kind whose nodal points do not coincide with those of the
electric oscillation, and that this oscillation, like the electrical
one, exhibits itself as a directive change of space-conditions,
but that the characteristic direction of the new oscillation is
perpendicular to the electrical one.

We may indeed, going beyond mere observation, at once
identify the new oscillation with the magnetic oscillation
required by theory. The rapidly alternating magnetic force
must induce in the closed hoop a current alternating rhyth-
mically with it, and the reaction between these causes the
deflection of the loop. The magnetic force has its maximum
value at the nodes of the electric oscillation, and just there its
direction is perpendicular to the plane of the bent wire. We
can most easily understand the repulsion between the fixed
wires and the neighbouring parts of the hoop by regarding it
as the effect of currents flowing along these paths. The
current deduced in the hoop must continually annul the efiect
of the inducing current in the interior of the hoop ; it must
therefore at every instant be in the opposite direction to the
latter, and must accordingly be repelled by it

All the remaining phenomena of disturbance which are
observed with the suspended hoop, can without difficulty be
connected with the above explanation. Under certain circum-
stances complications arise. For example, if we leave the

XII MECHANICAL ACTION OF ELECTKIC WAVES IN WIKES 193

arrangement in the state shown in Fig. 39, but move the hoop
from the node b V towards the antinode of the oscillation, the
repulsion rapidly diminishes ; at a certain distance it becomes
zero, and then changes into an attraction which increases until
we arrive at the antinode. In one special case, for example,
the repulsion at 6 ft' amounted to 20 scale divisions, disappeared
at a distance of 95 cm. from the end, and then changed into
an attraction of which the maximum value was measured by
44 scale divisions. Clearly these changes are not to be ex-
plained by the behaviour of the magnetic force alone, but by
the joint action of the magnetic with the electric force; of
these the latter preponderates considerably at c, the former at
h y. By eliminating the electric force we can confirm this view
and follow the course of the magnetic oscillation. For this
purpose we set up two other wires parallel to the wires a h and
a'}/, but only 20 cm. long, and in such a position that they are
symmetrical towards the wires ah and a'V with reference to the
position of rest of the hoop, as shown by the dotted lines a^ \
and a^ l^ in Fig. 40. We connect ai with a^ b^ and a' &' with
^/V* Clearly this almost annuls the electric action, but
scarcely affects the magnetic. In fact, we now observe that
at all distances the movable ring is repelled from the fixed
wires. This repulsion diminishes continuously from the ends
towards the middle of the oscillation ; it there reaches a minimum
which, in the particular instance referred to, amounted to 4
scale divisions. If the electric oscillation were a real sine-
oscillation, the magnetic force would necessarily vanish at its
antinode ; but we saw at once, from the distribution of the
electric force, that this simple assumption did not hold good,
and so we can easily understand the existence of a residual
magnetic force at the antinode of the oscillation.

As required by theory, the mechanical effects of the electric
and of the magnetic force prove to be, in general, of the same
order of magnitude; the preponderance of the one over the
other in each particular case is mainly determined by the
proportions of the neighbouring parts of the ring and of the
fixed conductors. The more these approximate to the state of
infinitely thin wires, the more the magnetic force comes into
prominence ; the broader the surfaces which are attached to
them, the more is the magnetic force overpowered by the

194 MECHANICAL ACTION OF SLECTBIC WAVES IN WIBES xii

electric force. It is evident, even from the simple examples of
forms of conductor which we have chosen for the detailed
investigation, that a conductor of any form whatever inside a
train of electromagnetic waves must be subjected to the action
of forces which are complicated and not always easy to under-
stand.

XIII

ON THE FUNDAMENTAL EQUATIONS OF ELECTRa
MAGNETICS FOR BODIES AT REST

(Gottinger Nachr. March 19, 1890 ; Wiedemann's Ami. 40, p. 577)

The system of ideas and fonnulse by which Maxwell repre-
sented electromagnetic phenomena is in its possible develop-
ments richer and more comprehensive than any other of the
systems which have been devised for the same purpose. It is
certainly desirable that a system which is so perfect, as far as
its contents are concerned, should also be perfected as far as
possible in regard to its form. The system should be so constructed
as to allow its logical foundations to be easily recognised ; all
unessential ideas should be removed from it, and the relations
of the essential ideas should be reduced to their simplest form.
In this respect Maxwell's own representation does not indicate
the highest attainable goal ; it frequently wavers between the
conceptions which Maxwell found in existence, and those at
which he arrived. Maxwell starts with the assumption of
direct actions-at-a-distance ; he investigates the laws according
to which hypothetical polarisations of the dielectric ether
vary under the influence of such distance-forces ; and he ends
by asserting that these polarisations do really vary thus, but
without being actually caused to do so by distance-forces.^
This procedure leaves behind it the unsatisfactory feeling that
there must be something wrong about either the final result or
the way which led to it. Another eflfect of this procedure is
that in the formulae there are retained a number of superfluous,

^ The same remark applies to v. Helmholtz's paper in vol. 72 of Crelle's
■JoumaZ, — not, indeed, throaghout, but as far as relates to the special valaes of
the constants, which allow the distance-forces to vanish from the final results,
-and which, therefore, lead to the theory here supported.

196 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

and in a sense rudimentary, ideas which only possessed their
proper significance in the older theory of direct action-at-a-
distance. Among such rudimentary ideas of a physical nature
I may mention that of dielectric displacement in free ether, as
distinguished from the electric force which produces it and the
relation between the two — ^the specific inductive capacity of
the ether. These distinctions have a meaning so long as we can
remove the ether from a space and yet allow the force to persist
in it. This was conceivable, according to the conception from
which Maxwell started ; it is not conceivable, according to the
conception to which we have been led by his researches. As a
rudimentary idea of a mathematical nature I may mention the
predominance of the vector-potential in the fundamental equa-
tions. In the construction of the new theory the potential served
as a scaffolding; by its introduction the distance -forces which
appeared discontinuously at particular points were replaced by
magnitudes which at every point in space were determined only
by the conditions at the neighbouring points. But after we
have learnt to regard the forces themselves as magnitudes of
the latter kind, there is no object in replacing them by poten-
tials unless a mathematical advantage is thereby gained. And
it does not appear to me that any such advantage is attained
by the introduction of the vector-potential in the fundamental
equations; furthermore, one would expect to find in these
equations relations between the physical magnitudes which are
actually observed, and not between magnitudes which serve
for calculation only.

Again, the incompleteness of form referred to renders it
more diflj^^ult to apply Maxwell's theory to special cases. In
connection: Vith such applications I have been led to endeavour
for some time past to sift Maxwell's formulae and to separate
their essential significance from the particular form in which
they first happened to appear. The results at which I have
arrived are set forth in the present paper. Mr. Oliver
Heaviside has been working in the same direction ever since
1885. From Maxwell's equations he removes the same sym-
bols as myself; and the simplest form which these equations^

^ These equations will be found in the Phil. Ma^. for February 1888.
Reference is there made to earlier papers in the JSlectincian for 1885, but this
source was not accessible to me.

XIII FOR BODIES AT REST 197

thereby attain is essentially the same as that at which I arrive.
In this respect, then, Mr. Heaviside has the priority. Never-
theless, I hope that the following ijepresentation will not be
deemed superfluous. It does not clajim to set forth matters in
a final form ; but only in such a manner as to admit of further
improvements more easily than has l^itherto been possible.

I divide the subject into two parts. In the first part (A)
I give the fundamental ideas and tlfe formulae by which they
are connected. Explanations will be added to the formulae ;
but these explanations are not to be regarded as proofs of the
formulae. The statements will rather be given as facts derived
from experience; and experience must be regarded as their
proof. It is true, meanwhile, that each separate formula
cannot be specially tested by experience, but only the system
as a whole. But practically the same holds good for the system
of equations of ordinary dynamics.

In the second part (B) I state in what manner the facts
which are directly observed can be systematically deduced
from the formulae ; and, hence, by what experiences the correct-
ness of the system can be proved. A complete treatment of
this part would naturally assume very large dimensions, and
therefore mere indications must here suffice.

A. The Fundamental Ideas and their Connection

1. Electric and Magnetic Force

Starting from rest, the interior of all bodies, including the
free ether, can experience disturbances which we denote as
electrical, and others which we denote as magnetic. The
nature of these changes of state we do not know, but only the
phenomena which their presence causes. Eegarding these
latter as known we can, with their aid, determine the
geometrical relations of the changes of state themselves. The
disturbances of the electric and the magnetic kind are so
connected with one another that disturbances of the one kind
can continuously exist independently of those of the other kind ;
but that, on the other hand, it is not possible for disturbances
of either of the two kinds to experience temporary fluctuations
without exciting simultaneously disturbances of the other kind.

UNIVERSITY

198 FUNDAMKNTAX EQUATIONS OP ELBCTROMAGNETICS xiii

The production of the change of state necessitates an expen-
diture of energy ; this energy is again released when the
disturbance disappears ; hence the presence of the disturbance
represents a stock of energy. At any given point the changes
of state of either kind can be distinguished as to direction,
sense, and magnitude. For the determination, therefore, of the
electrical as well as of the magnetic state, it is necessary to
specify a directed magnitude or the three components thereof.
But it IB an essential and important hypothesis of our present
theory that the specification of a single directed magnitude
is sufficient to determine completely the change of state
under consideration. Certain phenomena, e.g. those of per-
manent magnetism, dispersion, etc., are not intelligible from
this standpoint; they require that the electric or magnetic
conditions of any point should be represented by more than
one variable.^ For this very reason such phenomena are
excluded from our considerations in their present state.

That directed magnitude by means of which we first deter-
mine the electrical state, we call the electric force. The pheno-
menon by which we define the electric force is the mechanical
force which a certain electrified body experiences in empty
space under electrical stress. That is to say, for empty space
we make the component of the electric force in any given
direction proportional to the component of this mechanical
force in the same direction. By electric force at a point in a
ponderable body we understand the electric force at this point
inside an infinitely small cylindrical space, infinitely narrow as
compared with its length, bored out of the body in such a way
that its direction coincides with that of the force — a require-
ment which, as experience shows, can always be satisfied. And
whatever may be the relation between the force so measured
and the actual change of state of the body, it certainly must,
in accordance with our hypothesis, determine the change of
state without ambiguity. If we everywhere replace the word
" electric " by the word " magnetic," and the electrified test-
body by the pole of a magnetic needle, we obtain the definition
of magnetic force. In order to settle the sense of both forces
in the conventional manner, let us further stipulate that the
electrified test- body is charged with vitreous electricity, and

1 [See Note 29 at end of book.]

XIII FOR BODIES AT REST 199

that the pole of the magnetic needle used is the one which
points towards the north. The units of the forces are still
reserved. The components of the electric force in the directions
X, y, z, we shall denote as X, Y, Z, and the corresponding
components of the magnetic force as L, M, K

2. The Energy of the Field

The stock of electrical energy in a portion of a body,
within which the electric force has a constant value, is a
homogeneous quadratic function of the three components of
the electric force. The corresponding statement holds good for
the supply of magnetic energy. The total supply of energy
we shaU denote as the electromagnetic ; it is the sum of the
electrical and the magnetic.

According to this, the amount of energy of either kind per
unit volume is for an isotropic body equal to the product of the
square of the total force under consideration and a constant.
The magnitude of the latter may be different for the electric
and the magnetic energy ; it depends upon the material of the
body and the choice of the units for energy and for the forces.
We shall measure the energy in absolute Gauss's measure ; and
shall now fix the units of the forces by stipulating that in free
ether the value of the constants shall be equal to I/Stt, so
that the energy of unit volume of the stressed ether will be

OTT OTT

When the forces are measured in this manner, we say that
they are measured in absolute Gauss's units.^ The dimensions
of the electric force become the same as those of the magnetic
force. Both are such that their square has the dimensions of
energy per unit volume ; or, expressed in the usual notation,
the dimensions of both are M'^^L-^/^T-^

For every isotropic ponderable body we can now, in accord-
ance with what has been stated, put the energy per unit
volume as equal to

i-(X2 + Y2 + Z2) + ^(P + M2 + N2).

OTT OTT

1 See H. Helmholtz, Wied. Ann. 17, p. 42, 1882.

200 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

The new constants {e and fi) here introduced are necessarily
positive, and are simply numbers. We shall call e the specific
inductive capacity (DieUktricitdtsconstante) and fi the mag-
netic permeability (Ma^ndisirungsconstante) of the substance.
Clearly e and fi are numerical ratios, by means of which we
compare the energy of one material with the energy of another
material A definite value of either does not follow simply
from the nature of a single substance itself. This is what we
mean when we say that the specific inductive capacity and the
magnetic permeability are not intrinsic constants of a substance.
There is nothing wrong in saying that these constants are
equal to unity for the ether ; but this does not state any fact
derived from experience ; it is only an arbitrary stipulation on
our part.

For crystalline bodies the energy per unit of volume will
be equal to

^(^nX^ + ^22^* + ^ssZ' + 2€i2XY + 2.^YZ + 2^,3X2)

By a suitable choice of axes either the one part or the other
of this expression can be transformed into a sum of three
squares. It is even probable that the same choice of axes
would thus transform both parts. The e and /m must be such
that in the transformation into a sum of squares all the co-
efficients would become positive.

3. Connection of the Forces in tJie Ether

We assume that the system of co-ordinates is such that
the direction of positive x is straight out in front of us, the
direction of positive z upwards, and that y increases from left
to right.^ Assuming this, the electric and magnetic forces in
the ether are connected with each other according to the
following equations : —

^ Unfortunately for the English reader this is not the system employed by
Maxwell, but the symmetric one. Hence follow some differences from Maxwell's
formulae as to the signs + and - . The system is that which is employed in
V. Helmholtz's pai>ers.

XIII

FOR BODIES AT REST

201

f ,dL dZ dY

(3a)

dt
dU

dy
dX

A-r- = ^--

dt
d^S

dz
dY

A-Tr = -^-

dz '
dZ

~dx'
dX

(3b)

. ^X dU dN

dt
dY

dt dx dy^

A-77- = -i

dt
dZ

dx
dh

dy^
dJ^

dt dy dx*

in addition to which we have the equations (which are not
inconsistent with the above) —

_, tO. rfM dN ^

yZX dY dZ_
dx dy dz

as a supplement distinguishing the ether from ponderable
matter.

After these equations are once found, it no longer appears
expedient to deduce them (in accordance with the historical
course) from conjectures as to the electric and magnetic con-
stitution of the ether and the nature of the acting forces, — all
these things being entirely unknown. Eather is it expedient
to start from these equations in search of such further conjec-
tures respecting the constitution of the ether.

Since the dimensions of X, Y, Z, and of L, M, N are the
same, the constant A must be the reciprocal of a velocity. It
is in reality an intrinsic constant of the ether; in saying this
we assert that its magnitude is independent of the presence of
any other body, or of any arbitrary stipulations on our part.

We multiply all our equations by (l/47rA) . dr ; further
multiply the members of the series separately by L, M, K, X, Y, Z
respectively, and add all together. We integrate both sides of
the resulting equation over any definite space, of which the
element of surface dto makes, with the co-ordinate axes, the
angle n^jc, n^y, n^. The integration can be carried out on the
right-hand side of the equation, and we get —

d
di

/|^(X2 4-Y2 4.Z2) + ^(L24-M2 4-N2) |c?T

-— J{ (NY - MZ) cos n;jc + (LZ — NX) cos n,y
+ (MX — LY) cos n,z}d(o.

202 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

The integral on the left-hand side is the electromagnetic
energy of the space; the equation, therefore, gives us the
variation of this energy, expressed in magnitudes which relate
only to the bounding surface of the space.

4. Isotropic Non-Condiidors

In homogeneous isotropic non-conductors the phenomena
are qualitatively identical with those in free ether. Quantita-
tively they diflfer in two respects : in the first place, the
intrinsic constant has a value different from what it has in the
ether ; and in the second place, the expression for the energy
per unit volume contains, as already explained, the constants
e and /*. The following equations represent these statements,
and are in accord with experience : —

(4a) ^

dL _dZ dY

dt dy dz '

, ^M dX dZ

dt dz dy^

dt dz dy '
dY _dN dL

dt dx dz

, dZ dL dM
Ae — = — «

dt dy dx

For if, for a moment, we determine the measure of the
forces in the non-conductor as we have previously done in the
ether, and accordingly replace X, Y, Z by X/>^e, Y/j^e,
Z/^€, and L, M, N by L/^/^, M/^A^, N/^A^; then the
equations assume exactly the form of the equations for the
ether — with this single difference, that the magnitude A is
replaced by the magnitude A/ ^€fi. If we retain, on the other
side, our measure of the forces, we can consistently assign to
the energy the requisite value. For by carrying out the same
operations which we employed in the preceding section, we

get —

^^^ ^ (X2 + Y2 + Z2) + ^(L2 + M2 + N2)|dT

dtJ \

j--^J{(NY - MZ) cos n;e + (LZ - NX) cos n,y
4-(MX — LY) cos n;s}da).

XKI

FOR BODIES AT REST

203

The general statements by which we have been guided to
equations (4) no longer hold good when the non-conductor is
not homogeneous. The question therefore arises — Do our
equations hold good in this case ? Experience answers this
question in the affirmative; we may therefore regard the
magnitudes e and fi in equations (4^) and (4^) as variable from
point to point.

5. Crystcdline Non-Conductoi^s

We can obtain a representation of the processes that take
place in such bodies — whose structure diflFers in different
directions, but whose electromagnetic properties merge into
those of isotropic non-conductors as the eolotropy disappears
— by regarding the time-variations of the forces on the left
hand of our equations as perfectly general linear functions of
the space-variations of the forces of the opposite kind on the
right hand. The generality of form of these linear functions
and the choice of their constants is, however, restricted by
assuming that the same operation which has already furnished
us with an equation for the variation of energy will always
do sp, and by stipulating that the energy shall thereby be ex-
pressed in the form already established. By these considerations
we are led to the following equations, which, in fact, suffice for
the representation of the most important phenomena : —

(5J

(5b)

dt
dK

cQf^

rfL dM. dK

rfL

. K"'^ dt

/ rfL ajyi ass\ a a.

^\'*'^'^'^'^^~dt'^'*^'dt)^'^~

rfNN

dt)

, / rfX rfY dZ\

"^V" dt'^^^^'dl'^^'^'df)

■12 dt

'^■~dt

Af e„ -jT + e^ — .- + 6 — I

rfY

rfZ\
rfZ\

rfX
dt "^ ^"^ dt "*" ^^^ dt J

rfZ

dV.

~ dz'

rfX

rfZ

dx'

rfY

rfX

dy '

rfM

rfN

dy'

rfN

rfL

dz'

rfM

dy dx

204 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

The equation for the variation of the energy of a space
gives the same result as in sections j[3) and (4). Experience
also shows that it is not necessary to regard the € and fi in the
equations of the present section as being constant throughout
the space ; they may be magnitudes varying in any way from
point to point

6. Distribution of the Forces in Condtictoi^s

In the bodies hitherto considered, every variation of the
electric force appears as the consequence of the presence of mag-
netic forces. If within a finite region the magnetic forces are
equal to zero, every cause for such a variation is wanting ; and
any existing distribution of electric force remains permanently,
so long as it is left to itself and no disturbance reaches the
interior from beyond the limits of the region. The electric
forces do not behave thus in all bodies. In many bodies an
electric force when left to itself vanishes more or less rapidly
away; in such bodies magnetic forces or other causes are
necessary in order to restrain an existing distribution from
change. For reasons which will appear later, we caU such
bodies conductors. The simplest assumptions which we can
make with respect to them are these: In the first place,
that the loss per unit time experienced by an electric
force when left to itself is proportional to the force itself;
and, in the second place, that independently of this loss the
magnetic forces here tend to produce the same variations as in
the bodies hitherto considered. If we introduce a new constant
\, the first assumption allows us to assert that the force-com-
ponent X when left to itself will vary in accordance with the
equation —

Ae- = — 47r\AX.

This first assumption is supplemented by the second as
follows : — When magnetic forces are present, the variation will
take place in accordance with the equation —

, rfX clM d^ ^ ,^

Ae- = 47r\AX.

at dz dy

The constant \ is called the specific conductivity of the body,

XIII FOR BODIES AT REST 205

measured electrostatically. Its dimension is the reciprocal of a
time. Hence the magnitude ej^ifk is a time ; it is the time in
which the force when left to itself sinks to Ije of its initial
value — the so-called time of relaxation. Hr. E. Cohn first
observed and drew attention to the fact^ that it is this latter
time, and not \ itself, that is a second intrinsic constant of the
body under consideration; one that can be settled without
ambiguity and independently of any second medium.

These considerations lead us now, conjecturally, to the
following equations which are in accordance with experience : —

dL__dZ^dY: ( dK^dU dN

^ dt dy dz* \ dt dz dy ^ '

^ , , dTA dX dZ ■ ) ^ dY dN dL

<^^> \^^ ^7 = ^ -"^' ^^^> f' dt = rfL- dz -^ttXAY,

dN" dY dX. \ dZ dx rfM

V ^^ = "^""rfy"' \^'Tt^ dy-'d^^^'"'^^^'

Clearly these equations refer only to isotropic media ; it is,
however, unnecessary, as far as the hypotheses hitherto made are
concerned, that the bodies should be homogeneous as well. But
in order to represent accurately the actual distribution of
-the forces in a non-homogeneous body, our equations still need
to be supplemented to a certain extent. For if the constitution
of a body varies from point to point, the electric force when
left to itself does not in general sink completely to zero, but it
assumes a certain final value which is not zero. This value,
whose components may be X' Y' Z', we call the electromotive
force acting at the point in question. We regard this as
being independent of time ; in general it is greater, the greater
the variation of the chemical nature of the body per unit of
length. We take into account the action of the electromotive
force as follows : — Instead of making the diminution of the
electric force when left to itself proportional to its absolute
value, we make it proportional to the diflFerence which remains
between this absolute value and the final value. In the case,
then, of conductors whose structure admits of the production of
electromotive forces, our equations become —

^ With respect to this, and the manner in which the magnitude \ is here
introduced, cf. E. Cohn, Berl, Ber. 26, p. 405, 1889.

206 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS

XIII

^6e)

•<

r. dL _dZ dY

. dU dX. dZ

^"dt^Tz-^' <«<•)

. rfN dY dX

Am- -= •

dt dx dy

, dX rfM rfN

^'^-Tz-di>-'^^''(^-^'^'

^ dY (IN dL

. dZ dL dM , .,„ „,,

7. £olotropic Conductors

If the conductor behaves differently in different directions,
we can no longer assume that the diminution in each com-
ponent of the force when left to itself depends only upon this
same component; we must rather suppose that it is a linear
function of the three components. If we further assume that
when the conductivity vanishes, the equations reduce to those
of an eolotropic non-conductor, we arrive at the following
system : —

.( dl. im dlS\ rfZ dY

,^ , r / dij dM rfNN dX dX

/ dL ^M dS^_dY dX

^1^13 dt "'"'*28 dT-^f^~di)~di~d^'

/ dX dY dZ. _ cJM dS

^1*11 dt + ^12 dt ''" ^« ~dt) ~ ~<h~'dy

-4,rA{VX-X0 + VY-Y0-l-\3(Z-Z0},
/ d,X dY dZ\_(m dL

(7i,) -I ^V'^ di '^^^ dt'^^^'diJ'l^'Tz

-4,rA{X,,(X-X0 + X^(Y-Y0 + X^(Z-Z0},
/ ^ dY dZ\_dL_dM.

^ Vl^ dt ■*■ *23 "^ + ^33 ^ j - -fly -^

- 47rA{ \3,(X - X') + \IY - Y') -f- X^J^Z - Z') }.

It is highly probable that for all actual bodies \2~\p
\i ~ \2? \% ~ ^2- ^® ^^y regard the constants e, /a, X in the
equations of this section again as varying in value from place
to place.

XIII FOR BODIES AT REST 207

8. Limiting Conditions

It is easily seen that the equations (7^) and (7i,) include all
the earlier ones as particular cases ; and that even the equations
for the free ether can be deduced from them by a suitable dis-
position of the constants. Now since these constants may be
functions of the space, we are led to regard the surface of
separation of two heterogeneous bodies as a transition-layer, in
which the constants certainly pass with extraordinary rapidity
from one value to another, but in which this still happens in
such a way that even in the layer itself the above equations
always hold good, and express finite relations between the finite
values of the constants and the forces which also remain finite.
In order to deduce the limiting conditions from this hypothesis,
which is in accordance with experience, let us for the sake of
simplicity suppose that the element of the surface of separation
under consideration coincides with the icy-plane.

Disregarding for the moment the appearance of electro-
motive forces between the bodies in contact, we fin^, on
examining the first two of the equations (7^) and (7i,), that the
magnitudes

dX dY dM dL

dz dz dz dz

must, in consequence of our hypothesis, remain finite in the
transition-layer as well. Thus, if the index 1 refers to the one
side of the limiting layer, and the index 2 to the other side,
we must have

The components of the force which are tangential to the
limiting surface therefore continue through it without discon-
tinuity. Applying this to the third of the equatioils (7a) and
(7b), we further find that the expressions

dL dU dN ,

dX dY dZ , ^ ^ ^ ^ ^^ ^ „^

^13 d^ + ^23 -^ + «33 -^ + 47K\iX + X32Y + X33Z)

208 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS

XIII

must have the same value on both sides of the limiting layer.
This statement, which expresses the reciprocal dependence of
the normal components of the forces on both sides of the limiting
surface, assumes in the case of isotropic bodies the simple fonn

rfX, dK

dZ dZ

In the next place, if we do not exclude the appearance of
electromotive forces in the limiting layer, we have to observe
that, in accordance with experience, the component of these
forces which is normal to the limiting surface, i.e, Z', becomes
infinite in the transition-layer itself; and yet in such a way
that the integral yz'da; taken through the limiting surface retains
a finite value; this value we can obtain from experiments,
although these leave us in the dark as to the course of Z' itself.
We now satisfy the hypothesis of the present section by
assuming that, with L, M, N, X, Y, the magnitude Z — Z'
remains finite in the transition -layer. Z becomes infinite
there; nevertheless, we can allow dZ/dt to remain finite.
Furthermore, we put

(8e) fZdz =/Z'dz = <^i,2 ,

Let us now integrate the first two of the equations (7a) and
(7b) after multiplying by dz through the transition-layer. Since,
on account of the shortness of the path, the integral of every
finite magnitude vanishes, we obtain the conditions —

Applying these to the third of the equations (7 J and

(7b), we obtain as the conditions for the normal-forces, that

on both sides of the limiting surface, the values of the
expressions

xni FOR BODIES AT REST 209

(IL dM d^

dX dY dZ ,

+ \3,(Y-Y0 + X33(Z-Z');-

must be equal If the bodies on both sides of the limiting
surface are homogeneous, then the presence of the electro-
motive forces has no efifect upon the conditions by which the
forces existing on the two sides are connected.

Our limiting conditions are nothing else than the general
equations (7a) and (7b), transformed to suit special circum-
stances. We may, therefore, imagine every statement and every
operation relating to these general equations within a definite
region to be at once extended to the limits of heterogeneous bodies
within the region ; provided always that this procedure does
not land us in mathematical impossibilities, and therefore that
our statements and operations, either directly or after suitable
transformation, do not cease to be finite and definite. We
shall often avail ourselves of the convenience which arises
from this. And if^ in general, we dispense with proving
that all the expressions which arise are finite and definite,
it must not be supposed that this is because we regard such
proof as superfluous, but only because the proof has long
since been furnished, or can be supplied according to known
examples, in aU the cases which have to be considered.

Each one of the previous sections means an increase in
the number of facts embraced by the theory. The following
sections, on the other hand, deal only with names and notations.
As their introduction does not increase the number of facts
embraced, they are merely accessory to the theory; their
value consists partly in making possible a more concise mode
of expression, and partly also in simply bringing our theory
into its proper relation towards the older views as to electrical
theory.

210 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

9. Electric and Magnetic Polarisation

So far as our equations relate to isotropic media, each
separate one gives the value which a single one of the physical
magnitudes under consideration will have at the next moment,
expressed as a definite function of the conditions existing at
the present moment This fonn of the equations is very
perfect &om a mathematical point of view, for it enables us
to ascertain from the outset that the equations determine with-
out ambiguity the course of any process whatever that may
be arbitrarily excited. It also appears very perfect from a
much more philosophic standpoint; for it enables us to recog-
nise on the left-hand side of the equation the future state —
the consequence — while, at the same time, on the right-hand
side of the equation, it exhibits the present state — the cause
thereof. But those of our equations which relate to eolotropic
bodies have not this perfect form ; for, on the left-hand side,
they do not contain the variations of a single physical magni-
tude, but functions of such variations. Since these functions
are linear, the equations can certainly be thrown into the
desired form by solving them for the separate variations.
Another means to the same end — which, at the same time,
simplifies the equations — is by introducing the magnitudes
which we call polarisations. We put

(9c) iin = Mi2L + ^22M + /i23N, (V -( n2-- ■ -22- ■ ^23

)\^ = «12^ + ^22^ + ^23^'
^ = /^13^ + A*23^ + A*33^ > '^5 = €i3X + f23Y + ^83^;

and call the resultant of £, zn, XI the magnetic, and the
resultant of 3£, tj, g the electric polarisation. For isotropic
bodies the polarisations and the forces have the same direc-
tion, and the ratio of the former to the latter is the specific
inductive capacity or the magnetic permeability. In the case
of the ether polarisations and forces coincide. If we introduce
the polarisations on the left-hand side of our equations, then
each equation gives us the variation of a single polarisation-
component as the result of the forces instantaneously present.
Since the forces are linear functions of the polarisation, there
is no diflBculty in introducing the polarisations on the right-
hand side of the equations as welL We should thus have

XIII

FOR BODIES AT REST

211

replaced the particular directed magnitude — the force — ^which
we first used to determine the electromagnetic state, by
another directed magnitude — the polarisation — which would
serve our purpose as well, but not any better. The introduc-
tion of the polarisations and the forces side by side considerably
simplifies the equations ; and this is our first indication that, in
order to represent completely the conditions in ponderable
bodies, it is necessary to specify at least two directed magni-
tudes for the electrical condition and two for the magnetic
condition.

In order to simplify our equations further, let us put

ru = \^{X - X') + X,/Y - Y') + X,3(Z - Z'),

(9eK " = VX - XO + X^(Y - YO + X JZ - Z'),

U = X3,(X - X') + X3/Y - YO + X,3(Z - Z').

For reasons which will appear iii the next section, we call iCy
V, w the components (measured electrostatically) of the electric
current-density.

Our most general equations now take the form

(9.)^

df, dZ dY

A—:— =

A^--^--

A-rr- = ^-

d3i dK dN

— -3 47rA'!;,

dt dy dz *

dt dz

dm dX dZ
dt ^ dz dx'

(9b)-

dt dx

dL
dz

dZl dY dK

^d^ dL

•

dt ^ dx dy'

dt dy

= -^ J 47rAw,

and, on introducing the polarisations, the electromagnetic
energy per unit volume of any body whatever takes the form

^(3ex -h rjY -t- sz) + ^(£L +mu + hn).

OTT OTT

In these expressions there no longer appear any quantities
which refer to any particular body. The statement that these
equations must be satisfied at all points of infinite space,
embraces all problems of electromagnetism ; and the infinite
multiplicity of these problems only arises through the fact
that the constants €, /a, X, X', Y\ Z' of the linear relations
(9c), (9d), (9e) may be functions of the space in a multiplicity
of ways, varying partly continuously, and partly discontinu-
ously, from point to point.

212 FUNDAMENTAL EQUATIONS OF ELBCTROMAGNETICS xiii

10. Electricity and Magnetism

Let there be a system of ponderable bodies in which
electromagnetic processes take place, and which are separated
by empty space from other systems. Let us differentiate the
three equations (9^) with respect to x,y,z respectively, and
add ; we thus obtain for all points of the system the equation

d /dX dtl dS\ . (du dv dw^

dt\dx dy dz) \dx dy dz *

Let us multiply this equation by the volume-element rfr, and
integrate over the volume up to any surface, completely
enclosing the ponderable system. Let d^o be the element of
this surface, and let the normal to dfo make with the axes the
angles w,aj, 7i,y, n^. Since Uy v, w are zero at the surface, we
get

d r/dX dtl (i3\ ^ f

dtJ\l^'^-dy'^d^r''^dtJ^^'''''''^ + ^^^^

f /dii dv <^^^\ ,
J \dx dy dz/
= — 4:'7r/(u cos njjo + v cos n^y + w cos n;s)d(o = 0.

Hence, if e denotes a quantity which is independent of time —

(10a)-! )\dx^ dy^'d^n

=/(X cos n;)c + tl cos Uyy + S cos n,z)da) = 4:7re.

The quantity e is obviously a function of the electrical state
of the system — a function of such a kind that it cannot be
increased or diminished by any internal or external processes
of a purely electromagnetic nature. This indestructibility of
the quantity e — which also holds good for other than purely
electromagnetic processes, so long as these are restricted to the
interior of the system — has prompted the idea that e represents
the amount of some substance contained in the system. In
accordance with this idea we call e the amount of electricity
contained in the ponderable system. But we must allow e to

XIII FOR BODIES AT REST 213

be positive or negative, whereas the amount of a substance is
necessarily positive. For this reason the hypothesis has been
supplemented by assuming the existence of two electricities of
opposite properties, and making e mean the diflference between
the two ; or else a way out of the diflBculty has been sought
in assuming that e represents only the deviation of the amount
of electricity actually contained from the normal amount
But if e represents the quantity of a substance in one of these
forms or some other form, then each volume-element rfr must
furnish its definite share towards the total amount of e. Only
hypothetically can we distribute the volume-integral, which
supplies e, among the separate volume-elements. A possible
distribution — the first which suggests itself for the moment —
is that which assigns to the volume-element dr the quantity
of electricity —

1 fd3i dVl dS\ ,

4:7r\ax dy dz/

We shall caU the quantity of electricity thus determined the true
electricity of the volume-element ; in the interior of a body,
in accordance with this, we shall call the expression

1 /dJi dV) dS\

— ( 1 '-\ )

47r \dx dy dz /

the true volume-density, and at the surface of separation of
dissimilar bodies the expression

4:^1 (*2 "■ *i) ^^s n;)c -f- (X]^ - J^i) cos n,y + {^^ — 3^) cos n,z)

the true surface-density of the electricity.

Another possible distribution of e among the volume-
elements which suggests itself is that which we get through
observing that in empty space polarisations and forces are
identical, and that we can therefore write instead of (10^) —

(lOb)

47re =y(X cos 7i;c + Y cos n,y -f Z cos n;i)d(o
_ r/dX. dY dZ\

J \dx dy dz/

214 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

and furthermore, that we can regard the expression

1 /rfX dY dZ\
47r\(jU' dy dz/

as representing the share which the volume-element dr con-
tributes to e. Accordingly, we call the quantity of electricity
so determined the free electricity of the volume-element, and

I /dX dY rfZ
4'7r\rfA' dy dz

the free volume-density, and at surfaces of separation —
— {(Xg - X^) cos ?i,aj + (Yg - Yj) cos n,y + (Z^ - Zj) cos n;s }

the free surface-density of the electricity. The difference
between the true and the free electricity we caU the bound
electricity. Our nomenclature foUows the familiar nonaen-
clature which takes its origin from the view hitherto held as
to the existence of electrical action-at-a-distance.^ According
to this view, a part of the extraneous or " true " amount of
electricity introduced into a non-conductor remains " bound "
by electrical displacement ^ in the molecules of the surround-
ing medium; whereas the rest remains "free" to exert its
distance -action outwards. And yet in many respects our
nomenclature dififers from the usual one. But since the latter
is sometimes ambiguous and not always consistent, it was not
possible for me to find a system of notation which would in
aU cases harmonise with the common use of terms. The
common phraseology is also ambiguous in that it uses the
word electricity without further discrimination to denote some-
times the true, sometimes the free electricity ; and this even
when important statements are being made.

In accordance with what has been stated above, we denote
the integral

/(3i cos n^ + tl cos n,y + 5 cos n;&)da),
extended over any closed surface and divided by 47r, as the

^ [See Note 30 at end of book.]

2 This is not identical with our polarisations. [See the theoretical part of
the Introduction.]

XIII FOR BODIES AT REST 215

true electricity contained within this surface. The same in-
tegral extended over an unclosed surface we shall call the number
of electric lines of force traversing this surface in the direction
of the positive normal. By this notation we follow Faraday's
conception, according to which the lines of force are lines which
in isotropic homogeneous bodies run everywhere in the
direction of the prevailing force, and the number of which is
proportional to the magnitude of the force. It is true that by
our notation we have rendered this conception more complete
or precise in this respect, — that in aU bodies we make the lines
of force run everywhere in the direction of the polarisation, not
of the force, and that their density is in all cases proportional
to the magnitude of the polarisation, not of the force. It follows
from our definitions that the quantity of true electricity con-
tained in any space, multiplied by 47r, is equal to the excess of
the number of lines of force which enter the surface over the
number which leave it. Every line of force which has an
end must accordingly end in true electricity ; and we may
define the true electricity as the free ends of the lines of force.
If a given space in the neighbourhood of the surface over which
our integral extends is free from true electricity, then the value
of the integral is independent of the particular position of the
surface within this space ; it only depends upon the position of
the boundary of the surface. In this case, then, we denote
the value of the integral as being the number of lines of
force crossing the boundary line — any ambiguity remain-
ing in this expression being supposed removed by special
restrictions.

We shall next calculate the variation of the true electricity
^^ in a part of our system bounded in any way. Let d© again
be an element of the bounding surface of this part. We get

/ -I /v \detD C /du dv dw\ , /> v ,

(10c)^= " J \A~'^T"^lz)^'^'^ -y(t4co8n,a; + vcosn,y + tocos w,2)<ta>.

Now if our bounding surface runs entirely in bodies for
which \ is equal to zero, then u, v, w still vanish at the
surface, and hence the amount of true electricity contained in
the space bounded by it remains constant. Accordingly, true
electricity cannot by any purely electromagnetic process escape
from a space which is wholly bounded by bodies for which \ is

216 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

equal to zero. For this reason we call, and have called, such
bodies non-conductors. But if the bounding surface passes
wholly or partially through bodies for which X is not zero, it
becomes possible for the amount of electricity within -the space
so bounded to vary through purely electrical disturbances ; for
this reason we call bodies of this latter kind conductors* This
division of bodies into conductors and non-conductors has
reference therefore to the true electricity ; with reference to the
free electricity all bodies may be regarded as conductors (cf.
displacement-currents). The amount of a substance within a
given space can only vary by its passing inwards or out-
wards through the surface; and it is clear that a definite
amount of the substance must pass through each element
of the surface. Consistently with the fact that the amount
of electricity given by our integral passes per unit time
through every closed surface, we may assume that the amount

u cos n^ + V cos n,y + w cos ?i,2;

passes through unit surface of every surface-element. In
accordance with this assumption we call, and have called, u, v,
w the components of the electric current-density, and the integral

/(u cos n,x + v cos n,y + w cos n,z)d€o,

taken over an unclosed surface, the electric current flowing
through this surface. We must, however, lay stress upon this —
that even if we admit the materiality of electricity, the above
special determination of its flow in conductors embraces a further
hypothesis. Upon the system of disturbance found there can
be superposed an arbitrary current-system, closed at every
moment, without thereby altering the increase or decrease of
electricity at any point.

If a portion of our system has attained its present condition,
starting from the unelectrified condition, by purely electro-
magnetic processes, or if by purely electromagnetic changes it
can return to the unelectrified state, then in aU non-conductors
of this portion the true electricity is equal to zero. For such
portions we have, then, in addition to the general equations, the
following as limitations of the permissible initial conditions
which are not inconsistent with the general equations, viz. : —

XIII FOR BODIES AT REST 217

dX dtl d3

1 +-^ =

dx dy dz

for the interior of non-conductors ; and

(3E.^ — 3E^) cos n;)c + (IJg — IJ^) cos 7i,y + (S^ - 3i) cos n;z =

for the boundary between two heterogeneous non-conductors.

The magnetic phenomena can be considered in a manner
exactly analogous to the electric phenomena. Let us proceed
to examine these, with the assistance of the equations (9J.
We shall call

1 /dt dm dn\

4:ir\dx dy dz)

the true volume-density for the interior of a body; the
expression —

'4~{(*^2"-*^i) ^^^ ^,« + (ZTIg — ZHi) cos ?i,y + (Zt2 — 2Ti)cos n^\

the true surface-density of magnetism at the surface of separa-
tion of two bodies; and the integral of these magnitudes
extended over a definite portion of space, the true magnetism
contained in this portion. The integral

y(£ cos n^-^KXi cos n,y + ZT cos n,z)d(Oy

taken over an unclosed surface, we shall call the number of
magnetic lines of force penetrating this surface, or the boundary
of this surface. Further, we shall call

1 /rfL dU dS\
47r\cfec dy dz)

the free volume-density for the interior of a body ; and

1 ,

^ -| (Lg — Lj) cos nfic + (Mg — M^) cos n,y -h (Ng — N^) cos n^)

the free surface-density of the magnetism at the surface of
separation of two bodies. The distinction between conductors
and non-conductors here disappears; for the equations (9^
contain no terms corresponding to the u, v, w of equations (9^).
With respect to true magnetism all bodies are non-conductors ;

•J18 FUNDAMENTAL EQUATIONS OF ELECTEOMAGNETICS xiii

with respect to free magnetism all bodies may be regarded as
conductors.

Let us suppose that a system or a portion of it emerges
from the non-magnetic state through purely electromagnetic
processes, or can by such processes return to this state. For
such a system, or that portion of it, the following equations
obtain, viz. —

dt dm dZl

dx dy dz
for the interior of the bodies ; and
(^2 - *^i) cos n^ + (Zn^ - Zn^) cos n,y + (p-^ - ^^ cos 71,2: =

for the surface of separation of heterogeneous bodies. These are
supplementary to the general equations as consistent stipula-
tions respecting the possible initial conditions.

1 1. Conservation of Energy

Let S denote the electromagnetic energy of a volume r,
which is bounded by the surface g>. We can calculate the
variation of S by multiplying all the equations (9^) and (9i,) by
(l/47rA)rfT, then multiplying them separately in order by
L, M, N, X, Y, Z, adding all together, and integrating over the
volume T. We obtain

rrfS 1 /•
{llMdi ^ iirA] '<^^^ ^^^^ ^^^ 7i,a? + (LZ - NX) cos n,y

\ + (MX — LY) cos n^ ] d(o -/(tcX + i?Y + wZ)dr.

If we extend the space t over a complete electromagnetic
system, ie. as far as a surface at which the forces vanish, then
our equation becomes

^= -/(uX + vY + wZ)dr.

The conservation of energy accordingly requires that in
every system which is not subjected to external actions, an
amount of energy corresponding to the integral on the right-
hand side should make its appearance per unit time in other

XIII

FOR BODIES AT REST 219

than electromagnetic form. This requirement is satisfied by
experience, which further teaches us that each separate volume-
element dr furnishes towards the total amount of the trans-
formed energy the quantity

(uX + vY + wZ)dT,

and shows us in what form this energy makes its appearance.
Or rather, to speak accurately, experience does not show that
this is true in all cases, but provisionally in the following
special cases only. According to both theory and experience,
the amount of energy which appears per unit time and per unit
volume in the interior of a homogeneous isotropic conductor
takes the form

It is always positive and represents a development of heat
— ^the Joule effect. At the boundary between two homogeneous
isotropic bodies, the amount of energy per unit volume that
appears in the transition-layer takes the form

uX' + vY' + wZ'i

hence, by integration over the whole thickness of the transition-
layer, it follows that the quantity of energy which appears per
unit of surface at the boundary amounts to

{u cos n^ + V cos n,y + w cos n;i) . <^i 2 >

which expression is also confirmed by experience. This
expression may be either positive or negative ; it may corre-
spond either to an appearance or a disappearance of foreign
forms of energy. Either the transformed foreign energy is heat
in this case as well — the Peltier effect; in which case we
denote the effective electromotive forces as thermoelectric.
Or else chemical energy as well as heat is transformed ; in
which case we denote the forces as electrochemical. Let us now
consider any limited portion of our system and calculate for it
the increase of its total energy, i,e. of the quantity

-J +J{uX + vY + wZ)dT.
In accordance with what has been stated, we find that this

.1 1

220 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

increase is equal to an integral taken over the surface of the
space. The variation of the stock of energy in this (and there-
fore in any) space will therefore be correctly calculated if we
assume that the energy enters after the manner of a substance
through the surface^ and in such quantity that through every
such surface the amount

1 ,

—J \ (NY - MZ) cos n;xi + (LZ — NX) cos n,y

+ (MX - LY) cos n;s)

enters per unit of surface. A geometrical discussion of this
expression shows that our assumption is identical with the
statement that the energy moves everywhere in a direction
perpendicular to the directions of the magnetic and electric
forces, and in such amount that in this direction a quantity
equal to the product of the two forces, the sine of the enclosed
angle, and the factor l/47rA, passes through unit surface per
unit time. This is Dr. Poynting's highly remarkable theory
on the transfer of energy in the electromagnetic field.^ In
examining its physical meaning we must not forget that our
analysis of the surface-integral into its elements was hypo-
thetical, and that the result thereof is not always probable.
If a magnet remains permanently at rest in presence of
an electrified body, then in accordance with this result the
energy of the neighbourhood must find itself in a state of
continuous motion, going on, of course, in closed paths. In the
present state of our knowledge respecting energy there appears
to me to be much doubt as to what significance can be attached
to its localisation and the following of it from point to
point. Considerations of this kind have not yet been success-
fully applied to the simplest cases of transference of energy in
ordinary mechanics ; and hence it is still an open question
whether, and to what extent, the conception of energy admits
of being treated in this manner.^

12. Fonderomotive Forces

The mechanical forces, which we perceive between ponder-
able bodies in the electromagnetically stressed field, we regard

1 J. H. Poynting, Phil. Trans, 2, p. 343, 1884,
2 [See Note 31 at end of book.]

XIII FOR BODIES AT REST 221

as the resultants of mechanical pressures which are excited by
the existence of electromagnetic stresses in the ether and in other
bodies. According to this view the mechanical forces which
act upon a ponderable body are completely determined by the
electromagnetic state of its immediate neighbourhood ; and it
need not be considered what causes at a distance may have led
up to this state. We further assume that the presupposed
pressures are of such a kind that they cannot give rise to any
resultants which would tend to set the interior of the ether
itself in motion. Without this hypothesis our system would
necessarily be incorrect, or at least incomplete ; for without it
we could not in general speak at all of electromagnetic forces in
the ether at rest. It necessarily follows from this hypothesis that
the forces under observation, acting upon ponderable bodies,
must satisfy the principle of the equality of action and reaction.

The question now is — Whether pressures can be specified
answering these requirements, and capable of producing the
resultants which are actually observed ? Maxwell, and, in a
more general form, von Helmholtz have described forms of
pressures which satisfy all the requirements of statical and
stationary states. But these pressures, if assumed to obtain
for the general variable state, would set the ether itself in
motion. We therefore assume that the complete forms have
not been discovered, and, avoiding any definite statements as
to the magnitude of the pressures, we shall rather deduce the
ponderomotive forces with the aid of the hypotheses already
stated, of the principle of the conservation of energy, and of
the following fact derived from experience : — If the ponderable
bodies of an electrically or magnetically excited system, which
always remains indefinitely near to the statical cpndition, are
displaced with reference to one another, and if at the same
time the amount of true electricity and of true magnetism in
each element of the bodies remains invariable and behaves as
if attached to the element, then the mechanical work consumed
in the displacement of the bodies finds its only compensation
in the increase of the electromagnetic energy of the system,
and is therefore equal to this latter.^

It still remains an open question whether forms of pressure
can be specified which satisfy, generally and precisely, the

[1 See Note 32 at end of book.]

222 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

requirements which we have laid down. If this is not the
case, our body of hypotheses contains an intrinsic contradiction
which must be removed by correcting one or more of these
hypotheses. But at all events the necessary amendments are
of such a kind that their effect would not make itself felt in
any of the phenomena hitherto observed. And it must be
pointed out that if there is here something lacking in our
theory, it is not a defect in the foundations of the theory, but
in parts of the superstructure. For, from our point of view,
the mechanical forces excited are secondary consequences of
the electromagnetic forces. We could discuss the theory of
the latter without even mentioning the former ; as indeed we
have excluded from the discussion all other phenomena of minor
importance which result from the electromagnetic state.

B. Deduction of the Phenomena from the Fundamental

Equations

We divide the phenomena represented by our equations
into statical, stationary, and dynamical. In order that a pheno-
menon may rank as statical or stationary, it is necessary that
it should not determine any variations of the electric and
magnetic forces with time, ie. that the left-hand sides of the
equations (9J and (Q^j) should vanish. Furthermore, in order
that a phenomenon may rank as statical, it is also necessary
that it should not be accompanied by changes in time at all,
and hence, more especially, that it should not determine any
permanent change of energy into other forms. The sufficient
and necessary condition for this is that the quantities u, v, w
in equations (9^) and (9b) should also vanish.

Statical Phenomena

If in the equations (9^) and (9^) the left-hand sides and
also the quantities v,, v, w vanish, the system splits up into
two mutually independent systems, of which one contains only
the electric forces and the other only the magnetic forces. We
thus get two groups of problems, of which one is called electro-
statics, and the other might be called magnetostatics.

XIII FOR BODIES AT RlS&T/^^ttSt ^^Mj^

NIVERsiT
13. Electrostatics ' ***

In this section we shall disregard the occurrence of electro-
motive forces; for if these admit of the existence of the
statical state at all, their action is too weak to come into
consideration in the problems which are of interest. In con-
ductors, accordingly, in which the quantities \ do not vanish,
the forces X, Y, Z must vanish. In non-conductors the equations
(9 J take the form

^ dy dz dz dx dx dy

Hence the forces possess a potential <^, and can be put equal
to the negative differential coeflBcient of this potential. Since
the forces are everywhere finite, ^ is everywhere continuous ;
it can therefore continue right through the conductors, and is
then to be regarded as constant within these. At a surface of
separation the differential coefficients of <^ tangential to the
separating surface continue through it without discontinuity.
Again, if Cj^ denote the volume -density of the free electricity,
according to section (10) the potential if> satisfies everywhere
in space the equation A<^ = — ^ire^ . In free ether this
assumes the form A<^ = ; and after suitable transformation
for the surface of separation between heterogeneous bodies it
gives the condition

\dnJ 2 \dn)\

I -r- I — f -.- 1 = — ^irep

where eff denotes the surface-density of the free electricity.
From all these conditions it follows that the value of <f>,
within an arbitrary constant, is definite and equal to f{^^flT)dT,
the integral being extended over the whole space with due
regard to the surfaces of separation. Thus when the potential
and the forces are distributed in the same way in different
non-conductors, the free electricities are the same. But the
corresponding quantities of true electricity are different, and
for the interior of two homogeneous non-conductors they are
in the ratio of the specific inductive capacities. Restricting
ourselves for the moment to isotropic bodies, the condition

224 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

that the density of the true electricity in the interior of the
non-conductors should liave given values e^, is expressed by
the equation

dx\ ax J (ly\ ay J dz\ dzJ

4:'ire„,

which at the boundary of two isotropic bodies assumes the
form

/d<l>\ /d^^

'^{dn)r''(d^)r~*'^'^'"

where e„ denotes the surface-density of the true electricity.

Let us now direct our attention to the stock of energy in
an electrostatic system. We obtain this successively in the
forms

The integrations are here supposed to extend over all space
in which electrical stresses exist, and therefore up to the
boundaries where the stresses vanish, £uid the suitable trans-
formation of the integrals at the bounding surfaces is im-
plicitly assumed. When any motion of the ponderable bodies
takes place, and the amounts of true electricity attached
to the elements of these bodies remain constant, then,
according to section (12), the increase in the value of any one
of these expressions is equal to the work done by the
mechanical forces in this motion. Hence, if our system consists
of two quantities of electricity E^ and E^, separated by the ether
and at a distance E apart which is very great compared with
their own dimensions, and if their distance apart increases by
an amount rfE, the electric energy of the space decreases by an
amount

,,^^ ^^dR

Thus the expression E^Eg/R^ represents the mechanical
force with which the two electricities tend to move apart.

XIII FOR BODIES AT REST 225

Coulomb's law, which, in the older theories forms the starting-
point of every discussion, here makes its appearance as a
remote final result.

With regard to the general determination of the pondero-
motive forces, we must here content ourselves with the follow-
ing remarks: — The last two expressions obtained for the energy
are just those whose variations represent the work done by
the motion of bodies in ordinary electrostatics. Hence it
follows that from the variations of these expressions we can
calculate the values of those same forces which are the starting-
point of ordinary electrostatics and are tested by experiment.
In particular, it may be shown that an element of a body
which contains a quantity e of true electricity is acted upon
by the mechanical force-components eX, eY, eZ, We thus
return to the same statements by means of which we first
introduced the electric forces.

14. Magnetostaiics

The equations which connect the components of statical
magnetic forces are the same as those which obtain between
the components of statical electric forces. Hence all the state-
ments in the preceding section may, with the necessary changes
of notation, be repeated here. And if, nevertheless, the mag-
netic problems of interest are stUl distinct mathematically from
the electrostatic problems, this arises from the following
causes : —

(1) The class of bodies known as conductors is here
wanting.

(2) In no bodies, excepting those which exhibit permanent
or remanent magnetism, does true magnetism appear. Hence
in the interior of such bodies, provided they are isotropic, the
magnetic potential '>^ must necessarily and always satisfy the
equation

which at the boundary between two such bodies becomes

i'idn)ri^{didr^'

226 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

The eqaations which apply to the interior and the boundaries
of crystalline bodies are somewhat more complicated, but can
easily be given ; these equations have to be considered in dis-
cussing the phenomena of the so-called magne-crystallic force.

(3) The specific inductive capacity of all known bodies is
greater than unity ; on the other baud, the magnetic permea-
bility of many bodies is less than unity. We call such bodies
diamagnetic, and all others paramagnetic. The free magnetic
density at the surface of an isotropic body bounded by empty
space is equal to (1 —/a) times the force in the interior of the
body normal to the surface. The sign of the surface-magnetism
{Bdegung) of a diamagnetic body is therefore opposite to that of
a paramagnetic body when the sense of the force is the same.

The study of statical magnetism further acquires a peculiar
aspect, owing to the fact that iron and steel, which are the most
important substances in connection with magnetic phenomena,
do not fit in at all well with the theoretical treatment. These
substances exhibit permanent and remanent magnetism ; hence
the polarisation of the ponderable material is here partly
independent of the prevailing force, and therefore the magnetic
state cannot be completely defined by a single directed magnitude.
Again, the relations between the force and the disturbances
produced by it are not linear ; so that, for a double reason, our
theory does not include these bodies entirely within its scope.
In order to avoid excluding them entirely from consideration,
we replace them by the two ideal substances which approximate
most nearly to them — perfectly soft iron and perfectly hard
steel. We define the first as a substance which obeys our
equations, and for which the value of /* is very large. We
attain a nearer approximation by giving /* different values
according to the problem under consideration. We define
perfectly hard steel as a substance which obeys our equations,
whose magnetic permeability is unity, in whose interior true
magnetism can exist distributed in any way, provided always
that the total quantity of true magnetism existing in any such
piece of steel does not differ from zero.

Stationary States

The same conditions hold good for the state of stationary
disturbances in non-conductors as for the statical condition ; in

XIII FOR BODIES AT REST 227

conductors, which for the sake of simplicity we shall assume in
this section to be isotropic, the equations (9 J, (9^), (9c), which
here come under consideration, take the form

dy dz ' dz dy

dX dZ \ dN dL , ,

^-^=0-

dL dM , .

^ dx dy ^ dy dx

(15e) t^ = \(X-XO, t; = X(Y-YO, «^ = X(Z-Z').

Differentiating equations (15i,) with respect to x, y, z
respectively, and adding, we get

/- ^ V du dv . dtv ^

(i^d) :i-+:r+ 7" = ^'

dx dy dz

which equation, at surfaces where the currents vary abruptly,
takes the form

(1 5e) 0^2 — ^1) ^^^ ^^ + (^'2 "" '^1) ^^^ '^yV + (^2 "" '^i) ^^^ ^»^ ~ ^'

Combining equations (15^) and (15^) with equations (15^) and
(15c), W6 obtain a system which contains only the electric
forces. This can be treated without regard to the magnetic
forces, and gives us the theory of current-distribution. If the
components u^ v, w of the current are found, the treatment of
the equations (15^) further gives us the magnetic forces exerted
by these currents.

15. Distribution of Steady Currents

It appears from equations (15^) that, in the interior of the
conductor through which a current is flowing, the forces can
also be represented as the negative differential coefficients of a
function <^, the potential, which is determined by the following
condition, which must obtain everywhere : —

., _ ^ , ^^\ dxJ dy\ ay y dz\ dz/ dx

dy dz

228 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

At the surface separating two heterogeneous conductors this
equation takes the form

I - {\^'2 - \^\) COS 7i,y- (XgZ'g - \Z\) cos ti^

and hence at the boundary between a conductor and a non-
conductor the form

(15i,) -5- = —X' cos 71^ — Y' cos 71^ — Z' cos 71^.

In addition to these limiting conditions we have, according to
section (8), at limiting surfaces where the electromotive forces
become infinite, the further condition

!<f>i — (f>^ =y(X cos n^R + Y cos n;y + Z cos n;s)dn,
=J{Xf cos 7i;c + Y' cos 7i,y + Z' cos n;s)dn,

These conditions together determine <^ definitely within a con-
stant which remains dependent upon the conditions outside the
conductor. For homogeneous conductors the equations (15^)
to (15i) assume the simpler forms —

(15k) -^

A<f> = for the interior of the conductor,
V ( -? ) = X„( — ) for the boundary between two con-

-^ = f or the boundary adjoining a non-conductor,
dn

<^j — <^^ = (f)^ 2 ft^ 3, bounding surface where electro-
^ motive effects occur.

The equations thus obtained admit of immediate application
to problems on current-distribution in bodies of three dimen-
sions. Their application to lamellar conductors or to linear
conductors is easy, and gives the definition of resistance, Ohm's
law for closed circuits, Kirchhoflfs laws for branched circuits, as
well as the other laws relating to the distribution of steady
currents.

XIII FOR BODIES AT REST 229

16. Magnetic Forces of Steady Currents

In order to determine the forces L, M, N produced by the
current-components u, v, w, which are now known, we introduce
as subsidiary magnitudes the so-called components of the vector-
potential, putting

U=fV, Y=r-dr, W=&.

J r J r J r

The integrals are to be extended over the whole space ; thus it
follows from the conditions of the steady state that

dJJ dV dW_

^p "T~ — v.

dx dy dz

We now put

J \dz dy / \dx dzJ

'^ \dy dx ^

These quantities L, M, N are solutions of equations (lo^),
satisfv the eouation

and satisfy the equation

d\. m^ ^«o
dx dy d

If, therefore, the forces actually present differ from these, the
differences between the two still satisfy the conditions for the
forces of statical magnetism, and may be regarded as arising from
these latter; this, however, does not exclude the supposition
that the magnetism itself is due to currents. But if no statical
magnetism is present at all, the formulae above given represent
completely the magnetic forces present.

If we have only to deal with linear conductors, in which
the current i flows, then the expressions vdr, vdr, wdr in the
quantities U, V, W are replaced by the expressions idx, idy,
idZy where dx, dy, dz are the projections of the element ds of
the circuit on the three axes ; and the integrations must then
be taken round all the circuits. Suppose we wish to
regard the magnetic forces of the whole current as the sum
of the actions of the separate current - elements. In order

230 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

to simplify the formulse, let us suppose the element to be at
the origin and the point a/ y' / to be in the ic^^-plane ; then an
analysis of our integrals, which, as far as its results are con-
cerned, is admissible, gives for the action of the current-element
idx upon the point o/y'/ —

r Aidx \/

L = 0, M = 0, X = AiVf^;-7-.= —' -'

ay r" r

which formulae contain the expression of Ampere's rule and
the Biot-Savart law.

Wherever u, v, w vanish, i,e, everywhere outside the con-
ductor in which the current flows, the values of the forces
must in accordance with equations (15^) possess a potential "^^
to whose negative differential coefficients we can equate them.
If the forces arise from only a single closed linear circuit, this
potential can be expressed in the form

( 1 61,) "^ = — Aij -T-d(o + const.

where dw denotes the element of any surface through the
circuit, n the normal to this surface, and where the integration
is extended over the whole of the surface bounded by the
circuit. We here regard as positive that side of the surface
from which the current appears to flow in the direction in
which the hands of a clock move. For the negative differential
coefficients of the above expression can in all cases be brought,
by known methods of transforming integrals, into the forms
found for L, M, N". Except in the circuit itself these differential
coefficients are therefore everywhere finite and continuous ; and,
even if the integral contained in '9 becomes discontinuous at
the surface ©, the necessary continuity can always be conferred
upon ^ itself if we regard the constant contained in it as
having an infinite number of values, and employ a value
varying by 47rAi whenever we pass through the surface ©.
The potential itself thus attains an infinite number of values,
and changes in value by 47rAi each time we return to the
same point after passing round the circuit.

Various interpretations can be assigned to the integral

XIII FOR BODIES AT REST 231

VT^hich occurs in ^. In the first place, it can be regarded as
the potential due to a magnetic shell. By following out this
conception we arrive at Ampere's theory of magnetism. Again
we may, with Gauss, regard the value' of this integral at a given
point as the spherical angle which the circuit subtends at this
point. From this, by an easy transition, we arrive at the
following statement : — For any given point this integral repre-
sents the number of lines of force which proceed from an unit
pole placed at the point and are embraced by the circuit. We
may supplement this by applying the following statement to
the potential itself (including its manifoldness) : — The differ-
ence between its values at two points is equal to the product of
Ai into the number of lines of force which cut the circuit in a
definite direction when an unit pole is moved in any manner
from the one point to the other.

From our standpoint the last interpretation is the most
suitable; it also allows us, with the aid of sections (12) and
(14), to deduce the following conclusions: — Firstly, the meobani-
cal work which must be done in moving a magnet-pole, or a
system of unchangeable magnetism, in the neighbourhood of a
current whose strength is kept constant, is equal to the number
of lines of force of the magnet-pole or magnetic system which
cut the circuit in a definite direction, multiplied by the current
and the constant A. Secondly, the mechanical work which
must be done in moving a constant current in a magnetic field
is equal to the number of lines of force which are cut by the
circuit during the motion, multiplied by the current and the
constant A. Lastly, and in particular, the mechanical work
which must be done in moving a constant current 1 in the
neighbourhood of a constant current 2, is equal to the number
of lines of force proceeding from the circuit 2 which are cut
by the circuit 1 during the motion, multiplied by the current
in 1 and by the constant A. It is also equal to the number
of lines of force proceeding from the circuit 1 which cut the
circuit 2 during the motion, multiplied by the current in 2
and by the constant A. Both expressions lead to the same
result ; . we can prove this by representing the product of the
current in the one circuit and the number of lines of force
from the other circuit which pass through it, by an expression
which is symmetrical with reference to both. For let the

232 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

symbols t, cU refer to the circuit 1 ; and the symbols t', d^,
U', V, W, If, M', N' refer to the circuit 2. Then the product
of At into the number of lines of force from 2 which pass
through 1 is equal to

AiJ(JJ cos n^ + M' cos n,y + N' cos n;x)d^

= — AH/(U' cos s^ + V cos 8,y + W cos 8fZ)ds

— . 2 • •/ f /"^^^ ^>^ ^^s *'»^ + ^8 5,y cos sf,y + cos «;? cos ^^z,.,

where € denotes the angle between the two current-elements.
The expression obtained is symmetrical with respect to both
circuits. We know that in fact the variations of this expres-
sion — Neumann's potential of the one circuit upon the other
multiplied by A^n' — ^gives the work required for the relative
displacement of closed currents, and hence the ponderomotive
forces which exist between the currents when at rest. We
also know that this statement contains everything that can
with certainty be asserted respecting the ponderomotive forces
which arise between currents.

We shall next calculate the magnetic energy of a space in
which the stationary current-components u, v, w and the un-
changeable magnetic densities m are distributed, assuming the
restriction that no magnetisable bodies are present in the space.
If "^ now represents the potential of the magnetisms m, we
obtain the energy successively in the forms —

(16c)

— J(L^ + M^ + NVt

Af(^/dV dW ld'9\ , „/dW dV ld^\

A. [ r /a\ aw ia^\ ,,/i

=rJH-^-^-A'd^)+^K

dy A dx/ \dx dz A dy/

\dy dx A dz/ *

XIII FOR BODIES AT REST 233

\dy flte / '
1 [ /dL dU dN\ ,

= iAV"(Ui* + Vt? + Ww)dT + ^/'^mdr,
or, in the case of linear currents —

, = i^*//

':^-Usd^ + y^mdr,

where, in the first part of the last form, the integration is to be
carried out with respect to both ds and ds^, and is to include
all currents present. It is clear from this last form that the
displacement of unchangeable magnets with respect to un-
changeable currents does not alter the magnetic energy of the
space. Hence the mechanical work which is done in such a
displacement does not find its compensation in the variation of
the magnetic energy of the space, as it does in the case of the
displacement of uuchangeable magnets among themselves ; we
must account in some other way for the work which has
been done. It further appears from the same formula that
the relative displacement of currents which are maintained
constant does determine a change in the energy of the space,
which is equal to the absolute value of the work done. But
when we pay due regard to the signs, we see that this change
does not take place in such a sense that it can be regarded as
the compensation for the lost mechanical energy, but in the
opposite sense. Here again, then, we have to account for double
the amount of work which the mechanical forces do in the
relative displacement of the circuits. We shall return to this
at the end of the following section.

Dynamical Phenomena

From among the infinite number of possible forms of the
variable state, comparatively few groups of phenomena have
hitherto fallen under observation. We shall refer to these
groups without attempting any exhaustive and systematic
classification of the subject.

234 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

17. Induction in Closed Circuits

111 accordance with equations (9 J electric forces must
necessarily be present in a varying magnetic field In general
these forces must be very weak, for they contain the very small
factor A ; on this account they can only be detected through the
currents which they excite in closed circuits, or through their
cumulative action in very long linear circuits which are closed
to within a small fraction of their lengths. Hence the eflTects
which can be experimentally measured invariably give us only
the integral effect of the electric force in a closed circuit, i.e.
the mtegrBl/(Xdx + Ydi/ + Zdz) taken along a looped line.
According to a known method of transforming integrals, which
we have already used, this line-integral is equal to the surface-
integral

fi/dZ dY\ /dX dZ\ (dX dX\ )^

taken over any surface « bounded by the line in question.
Applying equations (9.) this expression becomes equal to

d [
A — I (C cos n;c + IH cos n^y + 2ft cos w;2;)rfft).

dtJ

We may express this in words as follows : — The electro-
motive force which manifests itself in a closed circuit is equal
to the variation per unit time of the number of magnetic lines
of force which traverse the circuit multiplied by A. In
particular, if the induction arises from a closed variable current,
and if it is assumed that no magnetisable bodies are present, then
according to the results of the previous section the induced
electromotive force is equal to the product of the Neumann's
potential of the two circuits on one another and the variation
per unit time of the inducing current, multiplied by A-. These
laws— of which the first is the more general — with their con-
sequences embrace all the phenomena of induction which have
been actuallv observed in the case of conductors at rest.

Induction in moving conductors lies beyond the range to
which the present dissertation is restricted. But as far as
linear conductors are concerned, the transition from the case of

XIII FOR 'bodies at REST 235

induction in conductors at rest can be made by the following
statement: — Whether the magnetic field in the immediate
neighbourhood of a closed circuit changes in consequence of
the motion of ponderable bodies, or in consequence of purely
electromagnetic changes of state, the electromotive force pro-
duced in the closed circuit is the same, provided the change in
the magnetic field in its immediate neighbourhood is the same.
In accordance with this and the previous statements, the induced
electric force in a conductor in motion is equal to the number
of lines of force which are cut by the conductor in a definite
direction per unit of time, multiplied by A. The product of
this electric force and of the current in the moving conductor
gives, according to section (11), the thermal or chemical work
done by induction in the conductor. It follows from the
results of the preceding section, if we pay due regard to sign,
that this is equal to the mechanical work which must be done
by the external forces acting upon the circuit. Hence, if a
current of constant strength is maintained in a circuit, and
this circuit is moved towards a fixed magnet, the thermal and
chemical energy developed in the circuit accounts for the
mechanical work done ; while the magnetic energy of the
system remains constant. But, on the other hand, if this
circuit is moved towards another in which a constant current is
maintained, the larger amount of thermal and chemical energy
developed in the one through the motion accounts for the
naechanical work done ; and the same extra amoimt of energy
which appears in the other circuit accounts for the diminu-
tion in the magnetic energy of the field. Or, to speak more
accurately, the sum of the former amounts of energy balances
the sum of the latter. This settles the point referred to at the
end of section (16).

18. Mectromagrietics of Unclosed Currents

With regard to the phenomena which are possible, this is
the richest region of all; for it includes all those problems
which we cannot apportion elsewhere as special cases. But
as far as actual experience is concerned, it is a region which
hitherto has been but slightly explored. The oscillations of
unclosed induction-circuits, or of discharging Leyden jars, can be

236

FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS

XIII

treated with sufficient approximation according to the laws of
the preceding section ; and so far only the electric waves and
oscillations of short wave-length, which have been discussed
in the earlier papers, strictly belong here. With regard to the
theoretical treatment of this section we must therefore refer to
these earlier papers — pointing out, however, that the splitting
up of the electric force into an electrostatic and an electro-
magnetic part does not in these general problems convey any
physical meaning which can be clearly conceived, nor is it
of any great mathematical use ; so that, instead of following
earlier methods of treatment, it will be expedient to avoid it.

19. Optical Phenomena in Isotropic Bodies

We include in optics those electromagnetic disturbances
which are purely periodic in time, and whose period does not
exceed a very small fraction, say the billionth (10'^^) part, of a
second. By none of the means which are at our disposal for
detecting such disturbances can we recognise the magnetic and
electric forces as such ; what we are able to detect are simply
the geometrical relations according to which the existing dis-
turbance is propagated in different directions with different
intensities. Hence the mathematical representation of the
phenomena may also be confined to following the propagation
of one of the two kinds of force, after eliminating the opposite
kind ; and it is immaterial which of the two is chosen for
consideration. If we restrict ourselves to homogeneous isotropic
non-conductors and eliminate in the one case the electric, in
the other the magnetic, force -components, we obtain from
equations (4^) and (4^,) the following equations : —

(19.) i

(PL

dL <m dJ^ _
Vdx dy dz '

(19b) {

A V -^ = AX.

d^Y

Avf-AZ,

dK rfY dZ_
^ dx dy dz

XIII FOR BODIES AT REST 237

The solutions of these, assuming that the disturbances are
purely periodic, are always solutions of the equations (4J and
(4]t)) 8.S well. From each of the two systems of equations (19 J
and (19i,) it can be seen that transverse waves are possible,
and that longitudinal waves are impossible ; each of the two
systems gives for the velocity of the possible waves the value

from each of the two systems the phenomena of rectilinear
propagation, of diffraction, of the interference of natural and of
polarised light can be deduced, and the different kinds of
polarisation can be understood. By returning tx) equations
(4J and (4^) it can be shown that the simultaneous directions
of the electric and the magnetic force at any point of a plane
wave are invariably perpendicular to one another.

Suppose that the surface of separation of two homogeneous
isotropic bodies coincides with the icy-plane. In accordance
with section (8), and bearing in mind that we are dealing only
with periodic disturbances, the following conditions obtain at
this surface of separation

(19,) -{ m\ = uI (19,)

Each of these systems of limiting equations, together with
the corresponding equations for the interior of both bodies,
gives the laws of reflection, of refraction, of total reflection, —
in fact, the fundamental laws of geometrical optics. From
each of them it follows that the intensity of reflected and
refracted waves is dependent upon the nature of their polarisa-
tion, and that this dependence, as well as the retardation of
phase of the totally reflected waves, is in accordance with
Fresnel's formulae. If we deduce these formulae from the
equations of the electric forces (19y) and (IQ^), it will be
found that the method of development corresponds with the
method of deducing these formulae as given by Fresnel him-
self. If we start from the equations of the magnetic force
(19 J and (19^), we approach the path by which F. Neumann
arrived at FresneFs equations. From our more general

238 FUNDA3IEXTAL EQUATIONS OF ELECTROMAGNETICS xiii

standpoint we cannot only see from the start that both
paths must lead to the same goal, but we can also recog-
nise that the two are equally satisfactory. In the actually
observed phenomena of reflection the electric and magnetic
forces are not completely interchangeable, and the two paths
appear to be diflFerent. This is because the magnetic per-
meabilities are almost the same and equal to unity for all
bodies which come under consideration, whereas the specific
inductive capacities differ considerably ; and hence the optical
behaviour of bodies is chiefly determined by their electrical
properties.

If the iry- plane forms the boundary between our non-
conductor and a perfect conductor, the following equations
obtain in this plane : —

(19e) N = 0,

(19f) X = 0, Y = 0.

From these, together with the corresponding equations for
the interior of the non-conductor, it follows that for every
angle of incidence and every azimuth of polarisation the reflec-
tion is total. Since all actual conductors occupy an inter-
mediate position between perfect conductors and non-conductors,
the reflection from them may be expected to be of a kind
intermediate between total reflection and the reflection from
transparent bodies. Inasmuch as metallic reflection occupies
such a position, our equations appear adapted for giving a
general picture of metallic reflection as well. Up to the present,
however, investigation does not enable us to state how far
such a representation, by suitable choice of the constants, can
be extended into details.

It has already been pointed out in the first section that
the phenomena of dispersion require the introduction of at least
two electric or two magnetic quantities, and that they therefore
lie outside the limits of our present theory.

20. Optics of Crystalline Bodies

We shall confine our attention to optical phenomena in
the interior of a homogeneous, completely transparent crystal, —
in which we further assume that the axes of symmetry of the

XIII

FOR BODIES AT REST

239

electric and the magnetic energy coincide. Let the co-ordinate
axes be parallel to these common axes of symmetry, and, for
the sake of simplicity, let us write

^i> ^2» ^3> H'v /^2» fH* instead ot e^, €221 633, fin, ii^^ ^33.

Equations (5J and (5^,), which here come under consideration,
now take the form

dh dZ dY

(20J

Vi-^ = :7--

dt
dM

dy
dX

^H'l j^ — ^^ ~

dz
dY

Vs-rr = :yr -

dz
dZ

dx
dX

(^oy

dt dx dy

^'^ dt -

dM.
dz

^' dt -

. rfZ

dM.

I ^dt

These equations are integrated by assuming that the light
consists of plane waves of plane-polarised light, corresponding
to the following statements : — The magnetic force is perpen-
dicular to the electric polarisation, and the electric force is
perpendicular to the magnetic polarisation. In general the
direction of both forces does not coincide with the wave-plane ;
the direction of both polarisations lies in the wave-plane. Hence
the direction which is perpendicular to both polarisations is the
wave-normal ; the direction which is perpendicular to both forces
is the direction in which, according to section (11), the energy
is propagated ; in optics it is called the ray. To every given
position of the wave-normal there correspond in general two
possible waves of different polarisations, difierent velocities, and
different positions of the corresponding rays. If we suppose that
at any given instant plane waves starting from the origin of co-
ordinates proceed outwards in all possible directions of the wave-
normals, these wave-planes after unit time envelop a surface, —
the so-called wave-surface. Each single wave-plane touches
the wave-surface at a point on the corresponding ray from the
origin. The equation to the surface enveloped by the wave-
planes is found to be

(20e)

+ -)(- + - + -) 1

1 *>

x^ / 1

e^ti^^e^H'z €^1/ eg/igXei/Ag €ofii

htJi'J

^i^iHtHIHH

= 0.

240 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiii

The surface of the fourth degree represented by this equation
cuts each of the co-ordinate planes in two ellipses. In one of
the co-ordinate planes the two ellipses intersect each other in
four points — the four conical points (Naidpunkte) of the sur-
face ; in the two other co-ordinate planes one of the ellipses
surrounds the other ; and these statements hold good whatever
the values of € and fi are. To a very near approximation
^^ = ^ = ^ = 1 for all actual crystals ; in this case the general
form of the equation reduces to that of Fresnel's wave-surface,
and of the two ellipses in which the surface cuts the co-ordi-
nate planes, one reduces to a circle.

It is well known that the explanation of double refraction, of
reflection at crystalline surfaces, and many of the interference-
phenomena observed in crystals are intimately connected with
the consideration of the wave-surface and the simpler forms which
it assumes in special cases. But other facts, again, in crystallo-
graphic optics cannot be mastered by following out the idea of
a single electric and a single magnetic directed magnitude ;
hence these facts lie outside the present limits of our theory.

In sections (17) to (20) we have completed the enumera-
tion of those cases of the variable state whose importance has
up to the present time given rise to the development of special
theories.

XIV

ON THE FUNDAMENTAL EQUATIONS OF ELECTRO-
MAGNETICS FOR BODIES IN MOTION

( WiedemanrCs Ann. 41, p. 369, 1890)

An account which I recently published^ of electromagnetic
processes in bodies at rest agreed, aa far as the matter was
concerned, with Maxwell's theory, but as far as the manner
was concerned it aimed at a more systematic arrangement.
From the outset the conception was insisted upon, that the
electric and magnetic forces at any point owe their action to
the particular condition of the medium which fills the space
at that point ; and that the causes which determine the exist-
ence and variations of these conditions are to be wholly sought
in the conditions of the immediate neighbourhood, excluding
all actions -at- a- distance. It was further assumed that the
electric and magnetic state of the medium which fills space
could be completely determined for every point by a single
directed magnitude for each state ; and it was shown that the
restriction which lies in this assumption only excluded from con-
sideration comparatively unimportant phenomena. The intro-
duction of potentials into the fundamental equations was avoided.
The question now arises whether, while adhering strictly
to the same views and the same limitations, the theory can be
extended so as to embrace the course of electromagnetic pheno-
mena in bodies which are in motion. We remark, in the first
place, that whenever in ordinary speech we speak of bodies in
motion, we have in mind the motion of ponderable matter
alone. According to our view, however, the disturbances of
the ether, which simultaneously arise, cannot be without effect ;

1 See XIII. p. 195.
R

242 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

and of these we have no knowledge. This is equivalent to
saying that the question here raised cannot at present be
treated at all without introducing arbitrary kssumptions as to
the motion of the ether. Furthermore, the few existing
indications as to the nature of the motion of the ether
lead us to suppose that the question above raised is
strictly to be answered in the negative, for it appears to
follow from such indications as we have, that even in the
interior of tangible matter the ether moves independently of
it ; indeed, this view can scarcely be avoided in view of the
fact that we cannot remove the ether from any closed space.
If now we wish to adapt our theory to this view, we have to
regard the electromagnetic conditions of the ether and of
the tangible matter at every point in space as being in a
certain sense independent of each other. Electromagnetic
phenomena in bodies in motion would then belong to that
class of phenomena which cannot be satisfactorily treated
without the introduction of at least two directed magnitudes
for the electric and two for the magnetic state.

But the state of the case is diflFerent if we explicitly con-
tent ourselves with representing electromagnetic phenomena
in a narrower sense — up to the extent to which they have
hitherto been satisfactorily investigated. We may assert that
among the phenomena so embraced there is not one which
requires the admission of a motion of the ether independently
of ponderable matter within this latter ; this follows at once
from the fact that from this class of phenomena no hint has
been obtained as to the magnitude of the relative displace-
ment. At least this class of electric and magnetic pheno-
mena must be compatible with the view that no such dis-
placement occurs, but that the ether which is hypothetically
assumed to exist in the interior of ponderable matter only
moves with it. This view includes the possibility of taking
into consideration at every point in space the condition of
only one medium filling the space ; and it thus admits of the
question being answered in the affirmative. For the purpose
of the present paper we adopt this view. It is true that a
theory built on such a foundation will not possess the advan-
tage of giving to every question that may be raised the correct
answer, or even of giving only one definite answer ; but it at

XIV FOR BODIES IN MOTION 243

least gives possible answers to every question that may be
propounded, i,e, answers which are not inconsistent with the
observed phenomena nor yet with the views which we have
obtained as to bodies at rest

We therefore assume that at every point a single definite
velocity can be assigned to the medium which fills space;
and we denote the components of this in the directions of
^j y, ^ by a, yS, 7. We regard these magnitudes as being
everywhere finite, and treat them as varying continuously
from point to point. Of course we also admit discontinuous
variations, but we regard them as being only the limiting cases
of very rapid continuous variations. We further limit each
permissible discontinuity by the restriction that it shall in no
case lead to the formation of empty spaces. The necessary and
suflBcient condition for this is that the three differential coeffi-
cients da/dx, dfi/dy, dy/dz should everywhere be finite.
Wherever we find tangible matter in space we definitely de-
duce the values of a, j8, 7 from the motion of this. Wherever
we do not find in the space any tangible matter, we may
assign to a, jS, 7 any arbitrary value which is consistent with
the given motions at the boundary of the empty space, and is
of the same order of magnitude. We might, for example, give
a, j8, 7 those values which would exist in the ether if it moved
like any gas. We further use all the symbols which occur in
the preceding paper in the same sense here. We here regard
electric and magnetic force as signs of the condition of the
moving matter in the same sense in which we have hitherto
regarded them as signs of the conditions of matter at rest.
Electric and magnetic polarisation we simply regard as a
second and equivalent means of indicating the same conditions.
We also assign to the lines of force, by which we represent
these polarisations, precisely the same meaning.

1. Statement of the Fundamental Equations for Bodies in

Motion

At any point of a body at rest the time-variation of the
magnetic state is determined simply by the distribution of the
electric force in the neighbourhood of the point In the
case of a body in motion there is, in addition to this, a second

244 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

variation which at every instant is superposed upon the first,
and which arises from the distortion which the neighbourhood
of the point under consideration experiences through the
motion. We now assert that the influence of the motion is
of such a kind that, if it alone were at work, it would carry
the magnetic lines of force with the matter. Or more pre-
cisely: — Supposing that at any given instant the magnetic
state of the substance was represented in magnitude and
direction by a system of lines of force ; then a system of lines
of force passing through the same material points would also
represent in magnitude and direction the magnetic state at
any other time, if the effect of the motion alone had to be
considered. The corresponding statement holds good for the
variation which the electric polarisation experiences through
the motion. These statements suffice for extending to moving
bodies the theory already developed for bodies at rest ; they
clearly satisfy the conditions which our system of itself
requires, and it will be shown that they embrace all the
observed facts.^

In order to represent our ideas symbolically, let us first,
during the time-element dt, fix our attention upon a small
surface-element in the interior of the moving matter, which at
the beginning of this time-element lies parallel to the yz-'phjie,
and during the motion is displaced and distorted with the
matter. -We distribute and draw the magnetic lines of force
so that the number of them which penetrates the surface-
element at the beginning of the time dt is €. Everywhere and
always €, Zft, 2ft will then denote the number of lines of force
which traverse a surface-element of equal area parallel to the
yz, xz, icy-planes respectively. The number of lines of force
which traverses our particular surface-element now varies
owing to several causes; we shall consider separately the
amount which each separate cause contributes. In the first
place, the number would vary even if the surface-element
remained in its original position; this variation amounts to
{dtldt)dt, if dt/dt denotes the rate of variation of € at a
point which, with reference to our system of co-ordinates,
is at rest. In the second place, since the surface-element is
displaced with the velocity a, j8, y to places where other values

^ [See Note 38 at end of book.]

XIV FOR BODIES IN MOTION 245

of £ obtain, the rate of variation due to this cause amounts to
(adtldx + ^dt/dy + ydt/dz)dt. In the third place, the plane
of the element rotates with velocity da/dy about the 2;-axis,
and with velocity da/dz about the y-axis, and lines of force
will be embraced by the element which originally were parallel
to it ; the amount due to this cause is — (Vflda/dy + TXda/dzjdt
Finally the surface of the element increases with velocity
djS/dy + dyfdz ; and for this cause the number increases by an
amount t^d^jdy + dyldz)dt. If the sum of these quantities is
equal to zero, there can be no change in the number ; we have
therefore reckoned up completely all causes of variation, and
since all the amounts are very small, their sum represents the
total variation. We may also analyse the total variation in
another manner which has a more distinct physical significance,
viz. into the amount which the presence of the electric forces in
the neighbourhood, and the amount which the motion would
contribute, each by itself and in the supposed absence of the
other cause. According to the laws which hold good for
conductors at rest, the first amounts to (dZjdy — dYjdzyU . 1/ A ;
according to the statement which we have just made, the latter
is zero ; the first of itself represents the total variation. We
equate the two expressions found for the total variation,
divide by dt, multiply by A, add and subtract the terms
adTXi/dy + adXl/dz, rearrange the terms and thus obtain, after
treating similarly the other components of the magnetic force
and the components of the electric force, the following system
of fundamental equations for bodies in motion : —

' (dt d d^ , /d£ dm dn\\

dy dz '

(1.)

(dm d d /dt dm dn\]

dK dZ

dz dx

Un d d, fdt dm dXC\\

dx dy'

246 FUNDAMENTAL EQUATIONS OF ELECTKOMAGNETICS xiv

dX d d /dX dV rf^M

rfM dN
az dy

(U)

{dXl d d, /d3i rflj d^\

{

= :t- — -T:-47rAi;,
ax az

dL dU

= -1 ;-47rAt^.

ay dx

which are completed by the linear relations which connect the
polarisations and the current-components with the forces.
The constants of these relations are to be regarded as functions
of the varying conditions of the moving matter, and to this
extent as functions of the time as welL^

Our method of deducing the equations (IJ and (l^,) does
not require that the system of co-ordinates used should
remain absolutely fixed in space. We can, therefore,
without change of form, transform our equations from the
system of co-ordinates first chosen to a system of co-ordinates
moving in any manner through space, by taking a, fi, y to
represent the velocity -components with reference to the
new system of co-ordinates, and referring the constants
€, fi, X, X\ Y', Z', which depend upon direction, at every
instant to these. From this it follows that the absolute
motion of a rigid system of bodies has no effect upon any
internal electromagnetic processes whatever in it, provided that
all the bodies under consideration, including the ether as well,
actually share the motion. It further follows from this
consideration that even if only a single part of a moving
system moves as a rigid body, the processes which occur in this
part follow exactly the same course as in bodies at rest. If,
nevertheless, the existing motion does exert any influence
upon this part, this influence can only arise in those portions
of the system in which distortion of the elements occurs, and
must be propagated thence into those portions which move

^ [See Note 34 at end of book.]

XIV FOR BODIES IN MOTION 247

after the manner of rigid bodies. If, for example, a solid mass
of metal is suddenly displaced in the magnetic field, then,
according to our equations, the only direct or simultaneous
effect of this disturbance is upon the surface and the neigh-
bourhood of the metallic mass ; it here gives rise to electric
forces which afterwards produce secondary eflfects — penetrating
into the interior of the mass and giving rise to currents in it.

The equations here stated are in form and intention closely
related to those by which von Helmholtz in vol. IxxviiL of
Borchardt's Journal represented the behaviour of the electric
and magnetic forces in moving bodies.^ From this source the
notation is partly borrowed. And yet our equations differ
from those given by v. Helmholtz not only in form, but
also in meaning, at least with regard to such members as
have not hitherto been tested by experiment. Maxwell
himself does not seem to me to have aimed in his treatise at
any systematic treatment of the phenomena in moving bodies.^
The numerous references which he makes to such phenomena
are either confined to approximations, or relate only to cases
which do not involve any necessary distinction between the
theories of direct and of indirect action.

2. The Physical Meaning of the Separate Terms

Equations (1 J and (1|,) tell us the future value of the
polarisations at every fixed point in space or, if we prefer
it, in each element of the moving matter, as a definite
and determinate consequence of the present electromagnetic
state and the present motion in the neighbourhood of
the point under consideration. This is the physical meaning
of them in accordance with the conception which our system
represents. The common conception of the relations expressed
by these equations is quite different. It regards the rates of
variation of the polarisations on the left-hand side as the
cause, and the induced forces on the right-hand side as the

^ V. Helmholtz, Qes, Ahhandl, 1, p. 745 ; Borchardt's /owm. / McUfiem. 78^
p. 273, 1874.

^ [This statement is not quite correct. It does indeed hold good for Maxwell's
treatise, to which it refers; but in his paper "On Physical Lines of Force""
{Phil. Jfag.y April 1861) Maxwell has himself given a complete and systematic
treatment of the phenomena in moving bodies. Unfortunately I had not noticed
this when writing my paper.]

248 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS

consequence thereof. This conception has arisen through the
fact that the polarisations and their variations are usually sooner
and more clearly known to us than the forces which simultane-
ously arise ; so that, as far as our knowledge goes, the left-hand
sides of the equations are prior to the right-hand sides. In the
cases which chiefly interest us this conception has indeed very
great advantages ; but from the general standpoint it has the
disadvantage that the forces are not definitely determined
by the rates of variation of the polarisations of the opposite
kind, but contain terms which are independent of these varia-
tions. The common theory gets out of this difficulty by setting
these terms as electrostatic or magnetic forces in opposition to
the electromagnetic forces which are alone, according to that
theory determined by our equations. Although we do not
approve of such a separation, and hence do not accept the
common conception as to the causal relationship, it is still
interesting to show how the partial forces which are intro-
duced in the usual theory are contained in the separate terms
of our equations. For this purpose we split up the forces in
the form X = X^ + Xg, etc., L = L^ + Lg, etc., and put —

X = A(7m-y8«), L, =A(y85-7^X

(2)-[ Yi = A(aZl - tC), M^ = A(73e - aSl

Zi = A()8C - ami ^1 = A(arj - )83E),

We thus obtain for Xg, Yg, Z2, L2, Mg, Ng equations which
result from the equations (1^) and (1|,) for X, Y, Z, L, M, N
by omitting the second and third terms on the left-hand sida
Now the resultant of X^ Y^ Z^ is an electric force which arises
as soon as a body moves in the magnetic field. It is
perpendicular to the direction of the motion and to the
direction of the magnetic lines of force ; it is that force which
in a narrower sense we are accustomed to denote as the
electromotive force induced through motion. But it should
be observed that, according to our views, the separation of this
from the total force can have no physical meaning; for it
would be in opposition to our conception to suppose that the
magnetic field within a body could have a motion relative to it
The counterpart to the force Xj Yj Zj is the force Lj M^ Nj,
which must make itself felt in a non-conductor when the

XIV FOR BODIES IN MOTION 249

latter is displaced through the lines of force of an electric
field; but this is not yet confirmed by experience and is
absent from the older electromagnetics.

Let us now turn our attention to the resultant of Lg M2 Ng,
and suppose the general solutions of the equations containing
these quantities to be represented as functions of the quantities

u, d^jdt, a(dX/dx + dtl/dy + dSldz)y etc.

Let us put these latter quantities in the functions all equal to
zero ; there still remains a first part of the force which does
not owe its origin to electromagnetic causes. Its components
necessarily possess a potential; it represents that distance-
force which, according to the older view, proceeds from magnetic
masses. A second part of the force is given by that part of
the functions which vanishes when, and only when, u, v, w
vanish. It contains the magnetic distance-force which appears
to proceed from the actual electric currents. We obtain the
whole of the electromagnetic part of the force Lg Mg Ng by
replacing in the expression of the second part the quantity
4:'jrAu by the quantity

, . d2i , /d3i dD dS\

at \ax ay dz /

and treating v and w similarly. This corresponds to the state-
ment that as far as the production of a magnetic distance-
force is concerned, an actual current is to be regarded as
equivalent in the first place to the variation of an electric
polarisation, and in the second place to the convective motion
of true electricity. The latter part of this statement finds its
requisite confirmation in Eowland's experiment.

Finally, let us consider the force Xg Y^ Z^- W® ^^^
separate from this force as well a part which is independent of
time-variations of the system, which possesses a potential, and
which is treated as an electrostatic distance-force. From the
residue of the electromagnetic force which remains we can
detach a second part, which vanishes when, and only when,
the quantities dt/dt, d7Xl/dt, dXljdt vanish. It clearly repre-
sents the force of induction which arises from varying mag-
netic moments, but it also contains in a hidden form that
electric force which owes its origin tojiran^ing ,x:urrents.

^ OF THE ^

UNIVERSITT

250 FUNDAMENTAL EQUATIONS OF ELECTEOMAGNETICS xiv

Finally, there remains a third and last part which can be
interpreted as an electric force produced by a convective motion
of magnetism, and in which must be foimd the explanation
of certain known phenomena of unipolar induction.

These considerations show that we might also have arrived
at the system of equations (IJ and (1|,) by summing up the
effects of the separate forces required by the older theories,
and adding a series of hypothetical terms which can neither
be confirmed nor disproved by existing experience. The way
which we have followed requires a smaller number of inde-
pendent hypotheses. We now proceed to deduce from our
equations the most important general results.

3. Motion of Magnets and of Electrostatically Charged Bodies

As independent causes of variation of the electric or mag-
netic polarisation there appear in our scheme first the magnetic
or electric forces respectively, and secondly the motion of
material bodies. According to our conclusions in the case
of bodies at rest, the first cause produces no displacement of
true electricity in non-conductors and no displacement of
true magnetism at all. The latter cause of itself produces a
displacement of electricity and of magnetism towards the space
at rest, but it can cause no displacement towards the matter
in motion ; for by its motion this matter carries with it the
lines of force, and electricity and magnetism may be regarded
as the free ends of these lines. Hence when both causes act
together there can be no relative motion of true magnetism
with reference to the surrounding matter; nor can there be
any such relative motion of true electricity, at any rate in
non-conductors. Under these circumstances electricity and
magnetism move with the matter in which they are present,
as if they were indestructible and adhered firmly to the parts
thereof. In order to represent this same idea symbolically, let us
differentiate first the equations (1 J and then the equations (1^)
with respect Ui xyz, multiply by the volume-element dr which
we suppose to remain at rest, and to which the quantities
C, Zn, etc., refer. Let di^ denote a volume-element which at
every instant encloses the matter contained at the present
instant in dr ; let de! and dm- denote the amounts of true elec-

XIV FOR BODIES IN MOTION 251

tricity and true magnetism respectively contained in rf/, and
£', TXCy etc., the values of C, ZIT, etc., with reference to d-/. We
thus obtain —

.fd /di dTXl dU\
^dAdx'^^'^'d^)

^dx\dx^ dy '^ dzJ'^^d^Kdi'^'d^'^d^)

d_/di dm dXl^
dz \dx dy

(3.)

d_/d1L dm dU\
dz\dx dy dz)

\dx dy dz/Kdx dy dz/ J

d ( /di' dm' dn\ , , , dm' ^

^ (^(<^,^d3\
^di\dx dy dz)

d^/dX dtl d§\ o^/^ ^ ^\
dx\dx dy dz) dy\dx dy dz)

d/dX. dVl d3\

(3b) ■

dz\dx dy dz/

/da dp dy\/d3i dVl ^S\\^
\dx dy dz/\dx dy dzJ j

dy dz/ \dx dy

_dr/d3e drf_ ^g\ . de

dt ^\dx dy dz / f ^ dt
fdu dv dvj\

\dx dy dz)

These equations embrace the statements already made,
and complete them as far as conductors are concerned.
If the velocities a )8 7 are so small that the electric
and magnetic conditions may at each instant remain in-
finitely near to the stationary state, and if we restrict
ourselves to the consideration of such quasi-stationary states,
then the results which we have obtained are sufficient
and necessary to determine the interdependence of the
various states which may arise from each other. The intro-
duction of these results into such problems enables us to
replace the complete, but very complicated, equations (IJ and
(lb) l^y the equivalent and very simple equations which hold

252 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

good for statical problems in bodies at rest, and which can
be deduced from equations (IJ and (Ij,) by equating to zero
the velocities and the time-variations at all points of the space.
Such a simplification of the statements is not possible without
introducing the idea of electricity and of magnetism ; and it
seems to me that this is the principal reason why these ideas
are indispensable in the study of electrostatics and in the
representation of magnetic phenomena.

4. Induction in Closed Circuits

The greatest velocities which we can assign to the sur-
rounding bodies are so small compared with the velocity of
light — ^the reciprocal of which appears as the multiplier of
a, )8, 7 in equations (1 J and (1^,) — that electromagnetic effects
due purely to motion can only be investigated with precision
in the particular case in which these effects consist in the
induction of an electric current in a closed metallic con-
ductor. In order to determine the magnitude of such effects
in closed conductors, let us consider any unclosed portion a>
of a surface in the interior of the matter under consideration,
and which is displaced with the material particles during
the motion. Let s represent the instantaneous limiting curve
of this surface-element. Let f denote the number of mag-
netic lines of force which at any time traverse the surface w.
We shall again consider the causes which produce (independ-
ently of each other) a variation in f ' as being two — in the
first place, the electric forces ; and in the second place, the
motion of matter. If the first cause alone were at work, the
system would be at rest, and so the rate of variation of f
multiplied by A would be equal to the integral of the electric
force taken aipund the whole extent of s; the integral,
viewed from the side of the positive normal, being taken
clock-wise. If the motion alone were at work, it would not
produce any variation of f', for it would carry forward the
lines of force traversing the surface ct> together with this sur-
face itself Hence in the actual case in which the two
causes act together, the integral of the electric force taken
in the given sense around any closed curve s is equal to A
multiplied by the rate of variation of the number of mag-

XIV FOR BODIES IN MOTION 253

netic lines of force which traverse any surface which was
originally bounded by the curve s, but which follows the
motion. This law also holds good for the special case — the
only one which is important from an experimental point of
view — in which the curve s follows the path of a linear con-
ductor ; nor does it become invalid when the motion is sufi&-
ciently slow to allow all the states which arise to appear as
being steady, and the current as uniform in all parts of the
conductor.

To represent this symbolically, let n^^jo, n\y, n\z denote the
angle which the normal to the element dd of the moving sur-
face ft) makes at any instant with the axes. Let C ZH' Zl' be
the values o{ t Vfl Zl in this element. Further, let day, n,x,
n,y, n^ denote the values of doi, n'^Cy n\y, n' pi in the original
position. We observe that, from purely geometrical considera-
tions, we have

d ^ [ (^^ ^y\ ^0 ^7

~y:(d(o cos n^) = d(o< 1 3~ + T~ ) cos n;c — -7— cos n,y — — cos n^

d (da (da dy\ dy ]

jfd^ cos n ,z) = d<o\^ - ;^cos n;,: - -^ cos n.y+[-^ + ^) cos n^j.

and we thus obtain
d?' d

-^ = 3- 1 ( £' cos n';jc + 2TI' cos n',y + Zl' cos n'^m

di d£ di d'£\

+ a^— + p-j— + 7-3— Jcos n^ dm

j\dt ' " dx ' '^ dy ' ' dz J

I /dm dm. dm dm\

/•/<m dU dU dX{.\ , ♦

r /rf/3 dy\ ^ ( ^d^ ^ rdy

-f I \.[— + —]co^n^d(o— j t, — cos n,y da) — j ^-j-cosn^dco

— j Zn— cos n^dw \^ \-n- + J- J cos n^y dto— \ Zk— cos n;z d(o

f da f^dfi 7 (y>(da dfi\

— j Zt —cos UyX dw — jZl -j-cos n,y d(o + jZl \-- + i-joos n^ day ;

254 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

from which, with the aid of equations (1 J and (l^) we get

d}^ rf/rfZ dY\ /dX dZ\ /dY dX\

^VrJ\\dry^d^)'^'''''^\Tz'd^^
=/(Xdx-+Yrfy+Zffe),

the last integral being taken around the whole extent s of the
surface dxo.

In special cases these results admit of simplification. If it
is possible to shut off a singly connected space which entirely
contains the moving curve «, and in which there is no true
magnetism, it is clearly immaterial whether the auxiliary sur-
face c0 follows the motion of the material parts or sufifers a dis-
placement independently of these, provided it remains within
the space referred to, and is bounded by the curve s. In this
case we may more simply and yet definitely assert that the in-
tegral of the electric force taken around the closed curve is equal
to the time-rate of variation of the number of magnetic lines of
force embraced by the curve s, multiplied by A. If we retain
this same supposition, and if in addition the magnetic polarisa-
tion at every fixed point of the space is constant in spite of
the motion of the curve s, we may assert that the induced
force along the curve is equal to A multiplied by the number
of magnetic lines of force, considered as at rest, which the
curve s cuts in a given direction during its motion. If the
magnetic forces, under the influence of which the curve s
moves, are simply and solely due to the influence of an
uniform current along a path t, then the number of lines of
force traversing s is, as we have seen,^ equal to the product of
the Neumann's potential of the curves s and t, and of the
current in t. In this case, therefore, the variation in the
above-mentioned product per unit time multiplied by A gives
the electromotiVe force acting along the curve s.

In one form or another these theorems embrace all known
cases of induction which have been carefully investigated.
The laws of unipolar induction, too, can be easily deduced
from the general propositions. Quantitative investigations of
induction-phenomena in bodies of three dimensions have only
been carried out to a limited extent. The equations by which

^ See p. 232.

XIV FOR BODIES IN MOTION 255

Jochmann^ and others have succeeded in representing the
known facts, follow directly from our general equations by
omitting a number of terms which naturally disappear in con-
sequence of the special nature of the problem

We must not omit to mention that we may represent the
general theorem of induction in another and a very elegant
form if we allow ourselves to speak of an independent motion
of the lines of force, and to regard in general every variation of
the magnetic polarisation as the result of such a motion of the
lines of force. If we do this, we may state generally and
completely that the induced electromotive force in any closed
curve s is equal to the product of A into the number of lines
of magnetic force which are cut by the curve s in a definite
sense per unit time. But although no objection can be raised
to the occasional use of the conception therein involved,
nevertheless it will be better for us to avoid it in the present
paper. For the conception employed by Faraday, and developed
by Poynting,^ of a motion of the lines of force relatively to
the surrounding medium, is indeed a highly remarkable one,
and may be capable of being worked out ; but it is entirely
different from the view here followed, according to which the
lines of force simply represent a symbol for special conditions
of matter. There is no meaning in speaking of an independent
motion of such conditions. It should also be observed that
the controllable decrease and increase of the lines of force in
all parts of the space does not definitely determine the pre-
supposed motion of the lines of force. Hence the above-
mentioned proposition would not of itself decide definitely the
magnitude of the induction in all cases ; it should rather be
regarded as a definition by means of which one among the
possible motions of the lines of force is pointed out as the

effective motion.

5. Treatment of Surfaces of Slip

At the boundary of two heterogeneous bodies the electro-
magnetic constants may pass from one value to another dis-
continuously ; but the velocity - components ajSy do not

^ JochmanD, Crelle*8 J(mm, 63, p. 1, 1863.

2 J. H. Poynting, PhiU Trans, 2, p. 277, 1885. [See also Note 35 at end of
book.]

256 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS XIV

necessarily undergo discontinuous changes at the same time at
this bounding surface. The surfaces of separation between
solid bodies and fluids, or between fluids themselves, are to be
regarded as surfaces of discontinuity of this kind ; and we are
free to suppose that the transition at the boundary between a
body and the ether is of the same nature. The appearance of
continuous motion at such surfaces of discontinuity does not
give rise to any new considerations; the conditions of the
material parts on both sides of the surface are connected by
the same relations as those which obtain for bodies at rest.

But the case is dififerent when the velocity-components also
undergo discontinuous variations at the surface. As observed
in our Introduction, the discontinuity can only refer to the
components of the velocity which are parallel to the surface of
separation ; we therefore rightly denote surfaces of this kind
as surfaces of slip (Gleitjldchen). They may exist between
solid bodies which are in contact with one another ; it is also
occasionally convenient and — seeing how ignorant we are as
to the actual circumstances — permissible, to regard the surface
of separation between a body and the ether as a surface of
slip. As we have already remarked in the introduction, we
treat a surface of slip as the limiting case of a transition-layer
in which the motions, and possibly the electromagnetic con-
stants as well, change very rapidly, but still continuously from
one value to another. This conception is justified by the fact
that it does not lead to any results in contradiction with
experience; and it enables us to assert that the general pro-
positions which we have already deduced do not become
invalid in a system in which there are surfaces of slip. In
order that our conception may suffice to determine the conditions
in the surface of separation, the nature of the transition must be
subjected to certain general restrictions. We give these restric-
tions in the form of hypotheses respecting the finiteness of certain
magnitudes in the transition-layer itself. We assume that there
are no electromotive forces at the surface of slip. We place
the origin of the system of co-ordinates to which we refer at
any point of the element of the transition-layer under con-
sideration, and let it also follow this point during the motion.
We further give the 2J-axis such a direction that it stands
perpendicular to the element of the surface of slip, and also

XIV FOR BODIES IN MOTION 257

remains perpendicular during the motion. Thus the transition-
layer always forms the immediate neighbourhood of the ocfy-
plane. We assume that even in the transition-layer itself
the quantities

X Y Z L M N

36 r^ 5 t zn «

u V w a ^ ^

remain finite ; and in the same way that the differential co-
eflBcients of these quantities parallel to the surface of slip, i.e,
with respect to x and y, and also the differential coefficients of
the quantities

x r^ 5 c rn «

with reference to the time t, remain finite. On the other
hand, we should allow the differential coefficients with respect
to z to become infinite, with the exception of A^jdz, which, in
accordance of the remark in the Introduction already referred
to, must remain finite. Everywhere in the transition-layer,
accordingly, 7 itself is vanishingly small. These assumptions
being made, we multiply the first two equations of the system
(la) and (1|,) by dz, integrate with respect to z through the
transition-layer between two points lying exceedingly near to
it, and observe that, on account of the shortness of the
integration-path, the integral of every quantity which remains
finite in the layer vanishes. We thus obtain the following
four equations, in which the index 1 refers to the one side,
the index 2 to the other side, of the surface of separation —

2 2

f da f dfi

(5^) - Aj 3-^dz = Mg - Ml, Aj §-^dz = L2 - L^.

These equations give the mutual relations between the force-
components tangential to the surface of separation on both sides
of it. Here, as in the case of bodies at rest, the components
normal to the surface are connected by the condition that the
surface-density of the true magnetism at the surface of separation

258 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

cannot alter excepting by convection, and that the surface-
density of the true electricity can only alter either by convec-
tion or by an actual current

If the element of the surface of separation under con-
sideration is not charged with any true electricity or true
magnetism, S and Zt are constant in the interior of the transi-
tion-layer. In this case the equations (5,) and (5^) take the
simpler forms

(5,) X2-X,=AZX(A-A), Y,-Yi=A«(a2-aO,

(5a) L, - Li = A3(/92 " AX M^ - M^ = A3(ai - o^).

As an example of the application of these equations, let us
consider the case of a solid of revolution rotating about its
axis within a hollow in another solid body which closely
surrounds it. If this system is submitted to the action of
a magnetic field which is symmetrical with reference to the
axis of rotation, there will not be, according to our conception,
either in the interior of the rotating body, or in the interior of
the surrounding mass, any cause for the appearance of electric
forces. Such forces are, in fact, absent when the magnetic
excitement is entirely restricted to the interior of the one body or
of the other. But if the lines of force penetrate through the
surface along which the two bodies slide past one another, the
electromotive forces expressed by equation (5^) are excited at
this surface ; these forces spread into the interior of the bodies
and there produce the electric stresses and currents whose
existence is shown by experiment. If the bodies under con-
sideration are non-conductors and are subjected to the influence
of electric forces which are distributed symmetrically with refer-
ence to the axis of rotation, and which do not vanish at the
surface of slip, the introduction of the motion excites magnetic
forces in the neighbourhood in accordance with equation (S^).
It is true that effects of this kind cannot be observed with the
same certainty as those first referred to ; but there is at least
an indication of them' in Professor Eontgen's experiments.^

In the general case in which there are charges of true
electricity and true magnetism at the surface of separation, a
knowledge of the surface-density of these is not by itself
sufficient for ascertaining the integrals of the equations (5 J

^ W. C. Rontgen, JVied. Ann. 36, p. 264, 1888.

XIV FOR BODIES IN MOTION 269

and (5i,) ; beyond this it is necessary to know to what extent
the electricity and magnetism in the transition-layer share in
the motion of each of the two contiguous bodies. This
indeterminateness lies in the very nature of the matter.
Consider, for. example, Rowland's experiment on the effect of
the convective motion of electricity ; and suppose the electrified
disc to rotate within a solid insulator surrounding it closely,
instead of rotating in air. Clearly the magnetic effect would
diminish, even to the point of vanishing entirely, as the
electricity gradually escaped from the surface of the rotating
disc on to the contiguous surface of the body at rest.

6. Conservation of Energy — ^Fonderomotive Forces

We shall consider the transition of the system from the
initial to the final state during any element of time as being
split up into two stages. In the first stage we shall suppose
all the material parts to be transferred from their initial to their
final position, the lines of force simply following the motion of
the material parts. In the second stage we shall suppose that
the electric and magnetic forces, which by this time are
present, come into action, and in turn transfer the electro-
magnetic conditions into their final state. The variation which
tfie electromagnetic energy of the system experiences during
the whole period of transition is the siim of the variations
which it experiences during the two stages. The processes
which take place during the second stage are processes in
bodies at rest ; we already know how the variations of the
electromagnetic energy during such processes are compen-
sated by other forms of energy. But during the first stage,
too, the electromagnetic energy of each material part of the
system alters ; we have therefore to account for what becomes
of the electromagnetic energy thus diminished, or to find the
source of any increase. As far as all existing experience
extends, it can be proved beyond doubt that in every self-
contained electromagnetic system the amount of energy in
question is balanced by the mechanical work which is done by
the electric and magnetic ponderomotive forces of the system
during the element of time under consideration. But, never-
theless, taken as a statement of general applicability, this is

260 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

not sufficient to enable us to deduce generally and rigidly the
ponderomotive forces from the calculable variations of the
electromagnetic energy. For this reason we introduce two
further assumptions which are not inconsistent with it ; these
are not required by experience but by our own particular
views. The first assumption declares that the statement
already made — ^which experience proves to be correct for
every self-contained electromagnetic system — -also holds good
for any material part of such a system. The second assumption
asserts that no part of the system can exert upon the rest of
the system any ponderomotive forces excepting pressures which
are exerted by the elements of the first part upon the contiguous
elements of the remaining part, and which at every point
of the surface of contact depend simply upon the electro-
magnetic conditions of the immediate neighbourhood- The
pressures required by the second assumption are determined
without ambiguity by the first assumption ; we shall deduce
the magnitude of these pressures, and shall show that they are
sufl5cient to explain the facts which have been directly observed.
It then follows from the mode in which the pressures are
deduced that the principle of the conservation of energy is
satisfied in the case of moving bodies as welL

Consider during an element of time dt the magnetic energy
of a material particle, whose varying volume may be denoted
by di^, while dr denotes the value of dr^ at the beginning of
the time-element dt For the sake of simplicity let the origin
of our system of co-ordinates be placed permanently in a
material point of the space di^. If dr' moved as a rigid body,
carrying its lines of force with it, the amount of energy con-
tained in it would not alter. In general, therefore, the variation
of this energy must be simply a function of the distortion
which dr' experiences in consequence of the motion ; our
immediate problem is to represent the variation in this form.
Now it is not the polarisations alone which alter in consequence
of the distortions, but also the properties of the material
vehicles thereof, i,e. the magnetic constants. For the pur-
pose of calculating this variation we need a further extension
of our notation. In the first place, and in addition to the
constants /^, we define a series of constants fi by the condition
that

XIV FOR BODIES IN MOTION 261

CL + OTM + ZTN"

= fiiiL2 + 2fii2^M + etc.
= /Lti/Ca + 2fjLi2£m + etc.

These constants fi are therefore the coefficients of £, 2TI, H
in the linear functions of these quantities by which the forces
are represented. We further denote by f 97 f the displace-
ments which the point, whose velocities are a )8 7, suffers from
its original position at the beginning of the time dt The
quantities

d^ _ d^ dr) ^ 1

~i — ^jc> , + -; •^t/> etc.,

ax dy dx

are then the components of the distortions of the element dr'
in which the displacements ^ ^ f occur. The constants /^' are
functions of these quantities ; moreover, they depend upon the
rotations p, a, t which the element experiences during the dis-
tortion. During the element of time dt both ic^, Xy, etc., and
p, a, T remain vanishingly small; hence the dependence is
linear and is known to us, provided we are given the differential
coefficients of fi with respect to p, a, t, x^^ Xy, etc. The
differential coefficients with respect to p, o-, r can be calculated
from the instantaneous values of f/ itself. But this is not
possible for the differential coefficients with respect to x^^, Xy,
etc., and we must therefore assume that we are otherwise given
the quantities

W_ , ^^^^--u.' etc

~T~~ — H'U y 11> "TT — /*12 » 12i ®^^' 6^^'

The 36 constants so defined clearly correspond to the
magnetic properties of the particular substance which fills the
space dr in its instantaneous state of deformation. For our
purpose we cannot dispense with a single one of these constants;
nor can we d, priori deduce a single one of them from the
magnetic properties of the substance which we have hitherto
considered. By a suitable orientation of our system of co-

1 Cf. G. Kirchhoff, Mechanik, p. 123, 1877.

262

FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS

XIV

ordinates we can reduce the number of necessary constants ;
similarly a reduction takes place when there happen to be
symmetrical relations with respect to the system of co-ordinates
used. In the simplest case, in which the substance is not only
isotropic in its initial state, but also remains isotropic in
spite of every deformation that arises — viz. in a fluid, — the
number of the new constants reduces to a single one, which
then, together with the one magnetic permeability, sujficiently
defines the magnetic properties. Besides, it does not seem
improbable that even in the general case necessary relations
may be proved to exist between the constants which would
then reduce to a smaller number of independent constants.

This notation being now assumed, we obtain successively
the following expressions for the variation per unit time of
the amount of magnetic energy contained in the space dr^\ —

= iA^AU^^^ + 2y^/£aT + etc.)
OTT^ at

(6)

+ (£L+rnM+«N)^T'

4.-IK

dt dt dt /

+ (^f? + 2^J^f.m + etc.")
\dt dt J

From the last of these we proceed to remove the dif-
ferential coefficients with respect to t. We obtain the
following expressions for dt/dt, dVH/dt, dZl/dt from equations
(la) by considering only the influence of the motion in them,
and putting the velocities a, ^, 7, with due regard to the special
choice of our co-ordinate system, equal to zero —

dt \dy dz^ dy dz

dt \dz dx' dz dx

\dx dy' dx dy

XIV

FOR BODIES IN MOTION

263

For the magnitude dfi^^jdt we further have

dfi^^ __ rf/Ai/

dXj^ dfiii^ dx.
— -I- ,

dx^ dt dx,, dt

^ + etc.

■'X

+ etc.

dfiii dp

dp dt

_ , da f

— f^nii-j-'T'fhi ,12

dfiii /dy d^\

(da d^\
\dv dx)

+ etc.

^iw-u_f:2Z-'::^)+etc.

dp \dy dz /

We deduce similar expressions for dfii^jdt, etc. We in-
troduce all these expressions in the right - hand side of
equation (6), and this side now becomes a hom(^eneous
linear function of the nine differential coefficients oi al3y
with respect to xyz. But we can and will arrange this
function so that it shall appear to us as a homogeneous
linear function of the six rates of deformation dajdx,
dajdy + d^jdx, etc., and of the three rates of rotation
^da/dy-'d^/dx), etc. We here note that the coefficients of
the three rates of rotation must necessarily vanish identically ;
for a motion of a particle as a rigid body does not bring about
any alteration in the amount of energy contained in it.
Accordingly, we simply reject the terms in which these rates
of rotation occur, and thus obtain as our final result, after
reducing to the unit of volume by dividing by dr —

T- y ^(^I^ + ZnM + ZW)dr' ]
drdtlSTT J

^ ^^ ' £L - inM - ZtN + /Ai/,n ^ + ^f^liS^ + etc.)

(6a)

Sirdx
1 dl3

Sirdy

8vdz

Sir^dz dy'
1 /dy da\

STT^da; dz/
1 /da d£\
Sir^dy dx/

- £L + ZHM - HN + /hi',22<? + 2/*i2',22Cm + etc.)

- £L - mm + rtN + Ahi',8s£^ + 2^^\si^m + etc.)

Zm. + ZHN + /*ii',23«? + 2fiil^£m + etc.)
£N + XiL + Mn'.igC' + 2/ti2',i3£rn + etc.)
aiL + £M + fiu',n(^ + 2/ti2',i2£rn + etc.)

264 FUNDAMENTAL EQUATIONS OF ELBOTBOMAGNETICS xiv

Now it is clear that in the linear function of the rates of
distortion on the right hand the coefficient, taken negatively,
of each of these rates, gives that pressure-component with
which the magnetically strained matter tends to increase the
corresponding distortion. For let us, in accordance with the
usual ^ notation, denote by X^pX^X^ the components of the
pressure which the matter of the element dr exerts upon a
plane section perpendicular to the a;-axis ; and let us further
extend this notation to the directions of the other axes.
Then the expression

(Ix dy dz

represents the mechanical work, per unit volume and per unit
time, done by the material contents of the element dr in the
distortion which takes place. According to our assumption
this mechanical work is equal to the magnetic energy which
is lost as a result of the distortion. Inasmuch as this holds
for every possible deformation our assertion is shown to be
correct. Each of the pressure -components obtained is a
homogeneous quadratic function of the three components of
the prevailing magnetic force or, similarly, of the three com-
ponents of the prevailing magnetic polarisation. By exactly
analogous considerations we can deduce exactly analogous
expressions for the pressures which arise through electric
stresses. The total pressure is equal to the sum of the
magnetic and electric pressures.

Having now found the values of the ponderomotive pressures,
we add three remarks. The first remark has reference to the
difference between our system of pressures and the system
which Maxwell has given for the general case in which the
forces and the polarisations have different directions.^ In the
first place. Maxwell's formulae are simpler, because in deducing
them he paid no heed to the possible deformation of the
medium. A much more important difference consists in the
fact that the force-components which, according to the notation

^ G. Kirchhoff {Mechanik, Eleventh Lecture).
2 Maxwell, Treatise on Elect, and Mag., 2, p. 254, 1873.

XIV FOR BODIES IN MOTION 265

used, are denoted by X^, and Y^., have different values in
Maxwell, whereas with us they are identical. According to
our system each material particle, when left to itself, simply
changes its form ; according to Maxwell's system it would at
the same time begin to rotate as a whole. Hence Maxwell's
pressures cannot owe their origin to processes in the interior
of the element ; and they therefore find no place in the theory
here worked out. At the same time they are permissible, if
one starts with the assumption that in the interior of the
moving body the ether remains permanently at rest and
provides the necessary point of support for the rotation which
takes place.

The second remark has reference to the manner in which
our formulae become simplified when we apply them to bodies
which are isotropic, and which, in spite of every deformation,
remain isotropic — viz. to fluids. The system of constants
fi' here reduces to the one constant fjJ = l/fi. If we further
denote by a the density of the fluid, we have

f __ / __ f ^/^^ 1 ^/*

/^U , 11 — /^22 , 22 = f^SS , 33 = "" JT~ = T 3~i '

dloga- fjL^dloga-
f^u, 11 = etc. = 0.
Thus the pressure-components are —

X^=/^(-L2 + M2 + N2)- — ^^(L^ + M^ + N^X
OTT Sird log (7

(6b)JY,= ^( L^-M^ + N^)-—^^— (L^ + M^ + N^),

OTT OTra log (7

Z, = A( L^ + M^ - N^) ^ — (L^ 4- M^ + N^),

. Stt Sird log (7

Xj, = - Alm, X, = - Anl, y, = -^ mk

47r 4:7r 47r

For the same case quite identical formulse have already
been obtained by von Helmholtz^ by following a similar train
of thought. Our formulae merge into his if we alter the nota-
tion so as to replace L, M, N and fi by X/^, fi/^y v/^y and

1 V. Helmholtz, Wied. Ann,, 13, p. 400, 1881.

266 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

l+4v^, and further, notice that the of von Helmholtz's
forniulde is equal to d^jd log <r = dfij^ird log a}

The third remark has reference to the question, in how
far the resultants of the pressures deduced from our hypo-
theses are in accordance with the mechanical forces and couples,
which we actually observe in bodies subjected to electromag-
netic actions. We first observe that our observations are con-
fined to systems which are indefinitely near to the statical or
steady state. For such systems, however, the principle of
the conservation of energy is of itself sufficient to enable
us to calculate without ambiguity, from the loss of electro-
magnetic energy during any displacement, the magnitude of
the opposing mechanical force - components ; and it may be
regarded as already proved that the force -components so
calculated agree with those which are observed. One system
of force -components which satisfies the principle of the
conservation of energy is certainly given by the resultants
of the pressures which have been deduced. This system
must, therefore, be the one which is directly deducible
from that principle, and which is in accordance with experi-
ence. In order to arrive d, posteriori at the same result, we
observe that under actual circumstances the electromagnetic
pressures are much too feeble to cause noticeable deformations
of the volume-elements of solid bodies. The very slight dis-
tortions which they are able to bring about we are accustomed,
in the study of electricity, to treat separately as phenomena of
electrostriction, apart from the phenomena of electromagnetics
proper. If, therefore, we put on one side this special class of
phenomena, it wiU not affect the result whether we admit the
pressures as calculated by us in the case of solid bodies, or no
pressures at all, or any others of the same order of magnitude
We may, therefore, in general content ourselves with the
simpler formulae (G^,), in which we are now to take fi to mean iii
the case of crystalline bodies any constant of the order of
magnitude of /Aji, /irjg, etc. But we may further simplify the
formulae (61,) by neglecting the terms which contain the quan-
tity dfijd log (7. For these terms, which represent an unifomi
pressure, cannot produce any finite displacements in liquids on

^ The signs remain contrary, because v. Helmholtz reckons a tension as being
positive, whereas we reckon a pressure as positive.

XIV FOR BODIES IN MOTION 267

li i account of their small compressibility ; they can only give

rise to phenomena of electrostriction or magnetostriction re-

ii^ spectively. In the case of gaseous bodies these terms dis-

:■; appear, for the constant fi and the specific inductive capacity

■zr do not change appreciably with the density cr. Those pondero-

:l, motive forces which produce finite relative displacements of

rt : the bodies must accordingly be represented by the resultants

of the following pressure-system, which is to be regarded as

p!r acting everywhere : —

I If

1^'

> •

(6e)

OTT
OTT

OTT

Now this simplified system of magnetic pressures is just
Maxwell's. Maxwell has shown that this, together with the
corresponding electric system, embraces the observed pondero-
motive forces between magnets, steady currents, and electrified
bodies, and to his simple demonstration we may here refer.

It does not appear to have been observed that this system
of pressures in general only leaves the interior of a homo-
geneous body, especially of the ether, at rest, if the acting
forces possess a potential, i,e. if the prevailing conditions are
statical or steady. In the case of any admissible electro-
magnetic disturbance, the pressures found must set the interior
of the ether — which we have expressly supposed to be mov-
able — into motion, with velocities which we could calculate if
we had an idea of its mass.^ This result seems to possess
little intrinsic probability. And yet there is no reason, from
the standpoint of the present dissertation, why we should
abandon the theory on this account; for the result is not

1 MaxweU, Treatise (m Elect, wind Mag., 1873, 2, p. 256. The signs there
are opposite to ours, because Maxwell reckons a tension as being positive,
whereas we reckon a pressure as positive.

2 [See Notd 36 at end of book.]

268 FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS xiv

inconsistent with our hypotheses, nor yet with what experience
teaches us. The sinall quantity of air which remains even in
the highest vacua is amply sufficient to keep below perceptible
magnitude all currents that could be excited in such spaces
under the existing circumstances.

Finally, I wish to point out once more that I only attach
value to the theory of electromagnetic forces in moving bodies
here proposed from the point of view of systematic arrangement.
The theory shows how we can treat completely the electro-
magnetic phenomena in moving bodies, under certain restric-
tions which we arbitrarily impose. It is scarcely probable
that these restrictions correspond to the actual fects of the
case. The correct theory should rather distinguish between
the conditions of the ether at every point, and those of the
embedded matter. But it seems to me that, in order to pro-
pound a theory in accordance with this view at present, we
should require to make more numerous and arbitrary hypo-
theses than those of the theory here set forth.

(UHIVERSITT

SUPPLEMENTAKY NOTES

(1891)

1. [11. p. 29.]

It was V. Helmholtz, in his paper Ueher die Erhaltung der Kraft,
who first stated (in 1847) that the discharge of a Leyden jar is oscil-
latory. He arrived at this conclusion from its varying and opposite
magnetic effects, and from the fact that when one endeavours to
decompose water by electric discharges, both gases are developed at
both electrodes. Sir William Thomson arrived independently at
the same result from theoretical considerations. The mathematical
treatment of the problem given by him in the year 1863 (Phil
Mag. (4) 5, p. 393) still holds good to-day. We may further
mention the following among the more important early papers on
the subject : —

On the discharge of Leyden jars —

Feddersen, Fogg, Ann. 103, p. 69, 1858 ; 108, p. 497, 1859 ;
112,p. 452, 1861; 113, p. 437, 1861 ; 115, p. 336, 1862 ;
116, p. 132, 1862.
Paalzow, Fogg, Ann. 112, pp. 567, 1861; 118, pp. 178,

357, 1863.
V. Oettingen, Fogg. Ann. 115, p. 513, 1862; Jubelbd. p. 269,

1874.
G. Kirchhoff, Fogg. Ann. 121, p. 551, 1864; Ges. Abhandl.

p. 168.
L. Lorenz, JFied. Ann. 7, p. 161, 1879.
On the oscillations of open induction-circuits —

Helmholtz, Fogg. Ann. 83, p. 505, 1851 ; Ges. Abhandl. 1,
429. The theory is implicitly contained in this, but is
not explicitly applied to the special case of oscillations.
V. Helmholtz, Ges. Abhandl. 1, p. 531 (1869).
Bernstein, Fogg. Ann. 142, p. 54, 1871.
Schiller, Fogg. Ann. 152, p. 536, 1872.

2. [II. p. 34.]

At first I insulated carefully with sealing-wax, etc. But I
always found that, for all such experiments as are here considered,

270

SUPPLEMENTABY NOTES

the insulation afforded by dry wood is amply sufficient. In the
subsequent experiments no other means of insulation was used.

3. [II. p. 39.]

I expect that the action of the induction-coil partly depends
upon the fact that directly before the discharge it allows the potential
to rise very rapidly. Several accessory phenomena lead me to
believe that when this rapid rise takes place, the difference of
potential is forced beyond the point at which sparking occurs when
the difference of potential increases slowly; and that for this
reason the discharge takes place more suddenly and energetically
than when a statical charge is discharged.

4. [11. p. 45.]

These curves should be compared with the corresponding
resonance-curves which Herr V. Bjerknes has obtained by more
accurate experimental measurements {Wied, Ann. 44, p. 74, 1891).

6. [II. p. 49.]

This remark in my first paper shows clearly that I never con-
ceived the oscillations of my primary conductor as perfectly regular
and long-continued sine-oscillations. The value of the damping
has recently been carefully determined by Herr V. Bjerknes {Wied.

Fig. 40.

Ann, 44, p. 74, 1891). Fig. 40 shows, in accordance with the
results of his experiments, the kind of oscillation given by a
conductor similar to our primary conductor.
6. [II. p. 50.]

Just at this point there has crept into the calculation a fatal
mistake, the unfortunate effects of which extend even to some of
the subsequent papers.

The capacity C in the formula T = tt n/PC/A denotes the
amount of electricity which exists at one end of an oscillating con-
ductor when the difference of potential between the two ends is
equal to unity. Now if these two ends consist of two spheres which
are far apart from each other, and if their difference of potential is
equal to unity, then the difference of potential between each of
them and the surrounding space is equal to±Y2' Therefore" the
charge upon each of the spheres, measured in absolute units, is

SUPPLEMENTARY NOTES 271

found by dividing its capacity, i.e. its radius measured in centi-
metres, by 2. Hence we should here put = -^- cm., and not
= 15 cm. The period of oscillation, T, now becomes smaller in

the proportion of 1 : \/2, so that T is now equal to 1*26 hundred-
millionths of a second.

M. H. Poincar^, as already stated in the introduction, first drew
attention to this error (Comptes Eendus, 111, p. 322, 1891).

7. [II. p. 52.]

The result is about right, but the way in which it is deduced is
not sound. We have just referred [6] to an error in the calcula-
tion which would have to be corrected ; and beside this no account
is taken of damping through radiation. Indeed, I had not thought
of this when writing the paper.

8. [IV. p. 67.]

The complications here mentioned, and the starting of long
sparks by other much shorter ones, refer to the following pheno-
mena : — Let the primary coils of two induction-coils be placed
in the same circuit, and let their spark-gaps be so adjusted as
to be just on the point of sparking. Any cause which starts
sparking in one of them will now make the other begin to spark
as well ; and this quite independently of the mutual action of
the light emitted by the two sparks — which, indeed, can easily
be excluded. Sparking begins either in both, or else in neither of
them. Again, let a Topler-Holtz induction-machine, with a disc
40 cm. in diameter, be turned rapidly so as to give sparks having a
maximum length of about 15 cm. Now draw the poles 20-25
cm. apart, so that the sparking entirely stops; it will now be
found that a long crackling spark can again be regularly obtained
every time a small spark is drawn from the negative conductor,
either with the knuckle of the hand or with the knob of a Leyden
jar ; or the negative pole may be connected to a long conductor,
and sparks may be drawn from this with the same result. The
" releasing " spark may be quite short and weak ; if it is drawn
with the knob of a Leyden jar, the jar only appears slightly
charged. The same effect cannot be obtained by drawing sparks
from the positiye pole. The phenomenon must have been often
observed before ; but I have not found any mention of it in the
literature on the subject.

I can give no explanation of these phenomena. They clearly
have the same origin as the phenomena which Herr G. Jaumann
has described in his paper entitled " Einfluss rascher Potential ver-
anderungen auf den Entladungsvorgang " (Sitzungsberichte d. Akad. d.
Wissensch. zu JVien., Bd. 97, Abth. Ua. July 1888). Herr Jaumann
arrives at the conclusion that "not only the form, condition, and
potential diiSerence of the discharge-field," but also " the manner in
which the potential difference alters, and probably its rate of

272 SUPPLEMENTARY NOTES

alteration, materially influence the discharge/' It is to be hoped
that these phenomena will be further explained.

9. [IV. p. 73.]

Soon afterwards Herren K Wiedemann and H. Ebert showed
that the action of the light only affects the negative pole, and only
the surface of it (JFied, Ann. 33, p. 241, 1888).

10. [IV. p. 76.]

Somewhat later I succeeded in this. I had hoped to observe an
influence of the state of polarisation of the light upon the action,
but was not able to detect anything of the kind.

11. [IV. p. 79.]

By this I did not mean to say that I had not succeeded in
observing the action of light upon discharges other than those of
induction-coils ; but only that I had not succeeded in replacing
spark-discharges — the nature of which is so little understood — ^by
simpler means. This was first done by Herr Hallwachs (JFied. Ann.
33, p. 301, 1888). The simplest effect that I obtained was with
the glow-discharge from 1000 small Plants accumulators between
brass knobs in free air; by the action of light I was able to
make the glow-discharge pass when the knobs were so far apart
that it could not spring across without the aid of the light.

12. [VII. p. 109.]

The 12 metres are supposed to be measured in the direction of
the base-line. The space on each side of the base-line was clear up
to a distance of 3-4 metres, with the exception of an iron stove
which came within 1 '5 metres of it. I did not think at the time
that at this distance it could interfere at all.

13. [VII. p. 109.]

In this calculation as well the capacity is assumed to be that of
an end-plate, supposed to be hanging free in air ; this capacity was
experimentally determined by comparison with the sphere previously
used. For the reasons stated in Note 6, only the half of this
capacity should have been taken. Hence the period of oscillation,
as correctly calculated, is smaller than the value given in the

proportion of 1 : \/2. Thus the correct value of the period of
oscillation is almost exactly one hundred-millionth of a second.

14. [VII. p. 112.]

Here, as well as in all that follows, it is to be understood that,
in order to produce stationary waves in wires, not only must the
primary and secondary conductors be brought into resonance, but the
straight stretched wires must also be tuned to unison with both
of these. Only in this case does the whole length of the wire
divide itself clearly into half wave-lengths, and only in this case is
this beautiful phenomenon exhibited in its full development. This
condition seems to have escaped the attention of some observers
who have repeated the experiments on waves in wires.

SUPPLEMENTARY NOTES

273

15. [VII. p. 113.]

This has uot turned out to be true. In tubes of about 2 cm.
diameter, filled with dilute sulphuric acid, the waves travel quite
well and with the same velocity as in wires. Herr E. Cohn has,
moreover, shown that the inertia of the electrolytes cannot come
into play when the period of oscillation is of the order here
employed (Wted, Ann. 38, p. 217). The fact that these oscillations
are transmitted through electrolytes has been used by J. J. Thomson
for the purpose of determining their resistance (Proc, Boy, Soc. 45,
p. 269).

16. [VII. p. 114.]

The correctly calculated period of oscillation is one hundred-
millionth of a second. This, with a wave-length of 2*8 metres, gives
a velocity of 280,000 km. per second, or approximately the velocity
of light.

This is the final form, — although, of course, with much more
careful data, — which Messrs. E. Lecher {Wied, Ann, 41, p. 850)
and Blondlot {C, E. 113, p. 628) have adopted for showing that the
velocity of waves in wires is the same as the velocity of light. As
a matter of fact, however, this final form only shows the accordance
of theory and observation in the following respect : that in a simple
straight wire 2*8 metres long, and in a conductor of the form of
our primary conductor, the periods of oscillation are equal. But
the absolute value of the period of oscillation, and hence the
velocity, might on that account differ by the same amount in both
cases from the theoretical value ; and it must differ by the same
amount if the same causes produce equal retardations in both
conductors.

Hence this final form cannot be employed for the purpose of
removing doubts as to the existence of such a retardation.

The velocity assumed in the text depends much more upon the
experiments of Fizeau and Gounelle and Siemens, than upon the
calculation.

17. [VII. p. 118.]

It is not without interest to inquire how the interferences
should have taken place if the experiments had led to the conclusion
that the velocity in wires is equal to the velocity in air. This can
easily be deduced from the correct theory given in No. IX., together
with the aid of Fig. 31, and comes out as follows : —

100

250

—

400

■~"

■^

274 SUPPLEMENTARY NOTES

If the velocities were equal, there should still have been one
change of sign; but the further changes which the experiments
gave can only be explained by a difference in the velocities, or by
illusions due to reflections or disturbances in the neighbourhood.

18. [VII. p. 13L]

It should be observed that we are here only able to determine
the position of the magnetic force by the aid of theory. From the
experiments we cannot conclude that a second kind of force is
present together with the electric force. If we confine ourselves to
the experiments, we can only regard the expression "magnetic
force " as a short name for a certain mode of distribution of the
electric force. That this magnetic force produces effects which
cannot be explained by the electric force, is first verified by experi-
ments in No. XIL ; and, of course, only for waves in wires.

19. [VIII. p. 133.]

The wave-length measured depends, therefore, very much upon
the distance of B and C ; and hence upon the assumption that C is
quite accurately measured. If we assume that the position of G is
altered by general conditions of the surrounding space, the first node
should be placed nearer to the wall and we might obtain much
smaller values for the wave-length. But the experiments give no
reason for believing that the position of C is uncertain.

20. [VIII. p. 136.]

Lloyd's experiment is the optical analogue of the experiments
in which the primary conductor is gradually moved away from the
wall. The experiments of the first kind, in which we removed the
secondary conductor from a reflecting wall, have al^o found an
optical analogue in the beautiful experiments which Herr 0. Wiener
has published in his paper on "Stationary Light- Waves and the
Direction of Vibration of Polarised Light" (Wted. Ann, 40, p. 303).

As to the acoustic analogues, I find that the phenomenon which
forms the analogue to the experiments of the first kind was discovered
by N. Savart many years ago (see Fogg. Ann. 46, p. 458, 1839 ; also a
number of Seebeck's paper in the subsequent volumes). If a steady
source of sound is placed at a distance of 15-20 metres in front of a
plane wall, and if we listen near the wall (best with the aid of a reso-
nator), we find that the sound swells out at certain points — the
antinodes, — and becomes weak at other points — the nodes. A correct
analogue to the experiments of the second kind — in which the
primary conductor is moved — has been already given in the text.
Another analogue — in itself interesting — is the following. Take a
glass tube about 60 cm. long and 2 cm. in diameter and lower it
gradually over a Bunsen burner, of which the flame is not too large.
At a given depth the Bunsen flame will begin, but not without some
difl&culty, to make the tube sing loudly. Now bring the system
near to a wall. Quite near the wall the sound disappears; it

SUPPLEMENTARY NOTES 275

reappears at a distance of a quarter wave-length, and again vanishes
at a distance of half a wave-length. By very careful adjustment,
which up to the present I have not been able to secure at will, I
have been able to observe two further positions of sound and silence
at distances of half a wave-length. I do not know of any com-
plete explanation of this phenomenon. Probably it has some
connection with the fact that such a tube becomes silent if a
resonator, tuned to the same note, is brought near its end. This
last experiment is due — as far as I am aware — to Professor A.
Christiani (Verhandl. d. phys, Gesellsch. zu Berlin^ Dec. 15, 1882, at
end of the Fortschritte der Fhysik, 36).

21. [VIII. p. 136.]

This remark refers to the experiments with wires, which I was
arranging at the time when this paper was written. It has already
been stated in the introduction that the hope here expressed has
not been fulfilled.

22. [IX. p. 141.]

An error in sign in the original paper, to which M. L. de la
Eive drew my attention, has here been corrected.

23. [IX. p. 160.]

This calculation is based upon the observed wave-length of 480
cm. If this is not correct, the calculation must be altered
accordingly. With regard to the real value of the damping see
Note 5.

24. [X. p. 161.]

By the experiments in the following paper it is pretty plainly
proved that in the case of rapid variations of current the changes
penetrate from without into the wire. It is thereby made probable
that in the case of a steady current as well, the disturbance in the
wire itself is not, as has hitherto been assumed, the cause of the
phenomena in its neighbourhood ; but that, on the contrary, the
disturbances in the neighbourhood of the wire are the cause of the
phenomena inside it.

That the disturbances in the wire are connected with a regular
circulation of materal particles, or of a fluid assumed ad hoc, is a
hypothesis which is neither proved nor disproved by our experi-
ments ; they simply have nothing to do with it. We have neither
any right to oppose this hypothesis, nor have we any intention of
doing so, on the ground of the experiments here described.

25. [XL p. 177.]

In connection with these phenomena we may refer to the
observation which Herren Hagenbach and Zehnder have brought
forward as an objection to my interpretation of the experiment
{Wied, Ann. 43, p. 611). My meaning is that light behaves
just as the electric waves here behave ; but we must imagine
the dimensions of everything concerned in the experiment to

276 SUPPLEMENTARY NOTES

be reduced in the same proportion, not only the length of the
waves.

26. [XL p. 181.]

Herr W. Konig first pointed out that the analogy between the
reflection of electric waves from our grating and the reflection of
monochromatic light from the surface of dichroic crystals is much
more complete than the analogy which is drawn in the text. He
has also drawn attention to the relation between the action of our
grating and certain polarising effects of optical gratings (fFied, Ann.
37, p. 651, at the end).

27. [XL p. 182.]

Messrs. Oliver Lodge and Howard have actually succeeded in
showing the refraction and concentration of electric rays by means
of large lenses (PhU. Mag. 27, p. 48, 1889).

28. [XL p. 185.]

Since then the experiments have been exhibited objectively in
many ways. Herr R. Eitter has employed successfully a frog's
leg (JFied. Ann, 40, p. 53). Mr. Dragoumis has used Geissler tubes
(Nature^ 39, p. 548). Herr Boltzmann has given a very convenient
method in which a gold-leaf electroscope is used {Wied. Ann, 40, p.
399). Herr Klemen6i2 has used a thermo-element (JVied. Ann, 42,
p. 416). The method which is most elegant and best adapted for
demonstration, although it is far from being an easy one, is the
bolometer method which Herren H. Rubens and R. Ritter have
employed for exhibiting the experiments and for further useful
researches {Wied. Ann. 40, p. 55, and subsequent volumes).

29. [Xin. p. 198.]

And by more than one independent variable. The " force " and
" polarisation " in this paper are not to be regarded as two variables
in this sense ; for they are connected by a fixed linear relation. If
this relation is allowed to drop, by regarding it as a special case of
a general relation, then "force" and polarisation" may serve as
two variables. But it would be more convenient to introduce the
polarisation of the ether as the one variable, and the polarisation
of the ponderable matter as the other.

30. [XUL p. 214.]

According to this usual system of nomenclature it is undoubtedly
true that the amount of "electricity" on an insulated sphere
remains unchanged when the sphere is immersed in an insulating
fluid, or, speaking generally, when it is moved in any way through
insulating media. Hence we have denoted as " true " electricity
the magnitude which remains unchanged during such motion. The
distance-action of the sphere, and therefore the "free" electricity
does change during the motion.

31. [Xm. p. 220.]

Consider a steam-engine which drives a dynamo by means of a

SUPPLEMENTARY NOTES 277

strap running to the dynamo and back, and which in turn works an
arc lamp by means of a wire reaching to the lamp and back again.
In ordinary language we say — and no exception need be taken to
such a mode of expression — that the energy is transferred from
the steam-engine by means of the strap to the dynamo, and from
this again to the lamp by the wire. But is there any clear physical
meaning in asserting that the energy travels from point to point
along the stretched strap in a direction opposite to that in which
the strap itself moves ? And if not, can there be any more clear
meaning in saying that the energy travels from point to point along
the wires, or — as Poynting says — in the space between the wires ?
There are difficulties here which badly need clearing up.

32. [XIII. p. 221.]

In order to deduce the mechanical forces from the changes of
energy, we must impart virtual displacements to the bodies. Hence
we should have to use the equations for bodies in motion and not
for bodies at rest, and at present the former are not at our disposal.
By the aid of the experimental fact here assumed we are able to fill
up this gap for the statical and steady states satisfactorily.

33. [XIV. p. 244.]

This proof that the statements here made embrace the observed
facts, is also a proof of the statements themselves. They are there-
fore logically stated as facts derived from experience ; not as results
of any particular experiment, but as results of all the general
experience which we possess respecting such matters.

34. [XIV. p. 246.]

The meaning of the equations is exceedingly simple ; but their
external appearance is somewhat complicated. This led me to expect
that skilful mathematicians might be able to replace them by more
elegant forms. And in fact Signor Vito Volterra has succeeded in
representing by a single system of equations the phenomena for
bodies both at rest and in motion {II nuovo Cimento (3), 29, p. 53 ;
see also p. 147 ibid.)

35. [XIV. p. 255.]

A similar theory has also been developed recently by J. J.
Thomson (Phil. Mag. (5), 31, p. 149). In so far as this theory
and Poynting's lead to MaxwelPs equations, I would regard them
as special forms of "Maxwell's theory," although their conceptions
are undoubtedly not Maxwell's.

36. [XIV. p. 267.]

This does not necessarily imply an error in the theory, though
it does necessarily imply a lack of completeness in it. Moreover it
seems to be at the very root of our view, for it can be understood
without using the equations. Let us suppose a magnetised steel
sphere to rotate in free space about an axis which does not coin-
cide with the direction of magnetisation. It continually sends out

278 SUPPLEMENTARY NOTES

electromagnetic waves; it therefore gives out energy and must
gradually come to rest Now let us take an iron sphere at rest and
excite in it a rotary magnetisation by varying electric forces ; it will
easily be seen that the iron sphere must, conversely, begin to
rotate. Such conclusions scarcely seem probable. But in con-
nection with these matters we have scarcely any right to speak of
probability, — so complete is our ignorance as to possible motions of
the ether.

INDEX TO NAMES

Ampere, 230, 231

Bernstein, 269

Bezold, V. 2, 3, 54, 56

Biot, 230

Bjerknes, 17, 270

Blondlot, 12, 273

Boltzmann, 27, 276

Christiani, 275

Cohn, 28, 205, 273

CoUey, 29

Cornu, 17

Coulomb, 225

Dragoumis, 276

Ebert, 94

Elster, 4

Engler, 103

Faraday, 7, 19, 101, 122, 136

Feddersen, 29, 269

Fitzgerald, 3

Fizeau, 9, 114, 273

Fresnel, 136, 237, 240

Gauss, 138, 199, 231

Geissler, 32, 60

Geitel, 4

Gounelle, 114

Hagenbach, 17

Hallwachs, 4, 94, 272

Heaviside, 160, 196

Helmholtz, v., passim

Howard, 276

Jaumann, 271

Jocbmann, 255

Joule, 219

Kirchhoflf, 60, 261, 264, 269

Klemen5i6, 276

Kola^ek, 179

Konig, 276

Lecher, 12, 187, 188, 273

Lloyd, 136, 274

Lodge, 3. 161, 276

Lorenz, 60, 269

Maxwell, passim.

Mosotti, 23

Neumann, 60, 232, 234, 237, 254

Newton, 136

Oberbeck, 42

Oettingen, v. 269

Paalzow, 269

Peltier, 219

Poincare, 9, 17, 27, 271

Poisson, 23

Poynting, 139, 160, 220, 256, 277

Riess, 64

Righi, 4

Bitter, 186, 276

Rive, de la, 12, 13, 14, 16, 276

Ront^en, 95, 258

Rowland, 249, 259

Rubens, 186, 276

Riihmkorflf, 31, 60, 64, 173

Sarasin, 12, 13, 14, 16

Savart, 59, 230, 274

Schiller, 269

Seebeck, 274

Siemens, 9, 114

Thomson, J. J., 273, 277

Thomson, Sir W., 50, 269

Trouton, 13

Volterra, 277

Weber, 61

Wiedemann, 94

Wiener, 274

Zehnder, 17, 275

UNIVERSITT

Printed by R. & R. Clark, Edinburgh

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